According to the baseball almanac, lace means:
To hit the ball hard. "In the second inning [Claude] Ritchey laced a single out in left field." (The New York Times, Apr. 28, 1908; Barry Popik).
I understand that the noun lace is made by twisting together fabric, which could explain the origin of the usage of lacing drugs.
But where did this baseball term come from?
The verb lace of the sense given in the OED as:
transitive. Sport (originally Baseball). To strike (a ball) forcefully; to hit (a run, pitch, etc.) in this way.
is a semantic extension from the earlier sense given in the OED as 'to lash (a person) with or as though with a whip or cord; to beat, thrash' which is first attested in 1599 per the OED. Both meanings (subsenses) are grouped under the same numbered sense. (sense 7)
For the etymology, OED says that this sense is:
apparently by association with lash v.1
The verb lash for the sense 'to beat, strike with a lash, whip, †rod, etc.' is from 1398 per OED. For the etymology, OED says that lash may have initially derived from an onomatopoeia.
An onomatopoeic origin is possible, and is favoured by the early appearance of the parallel and nearly synonymous lush v.1; compare dash, dush, flash, flush, mash, mush, smash, smush, etc.
Note: Your own source, Baseball Almanac, notes that the first use of the baseball term lace is from 1887, which is one year earlier than the first citation in the OED, listed as 1888. Here is the citation from 1888 from the OED:
Richard Johnston pulled himself together and laced the ball down to the farthest corner of the centrefield.
Boston Daily Globe 12 June 5/2
One of the standard meanings of lace as a verb is "to hit hard." Here is the relevant definition in Merriam-Webster's Eleventh Collegiate Dictionary (2003):
lace vt ... 5 BEAT, LASH
Paul Dickson, The Dickson Baseball Dictionary (1989) reports that the term has appeared in the context of baseball since the late nineteenth century:
lace/lace one v. To hit the ball hard. 1st [cited occurrence] 1888. "Lace it out." (caption used in Thomas W. Lawson's The Krank)
Although Google Books does find a copy of Lawson's book, whose full title is The Krank: His Language and What It Means, it isn't searchable (despite its being 136 years old and, therefore, presumably, out of copyright). One source refers to this volume as "baseball's rarest book"; and as its title suggests, before fans came into popular usage, the slang term for baseball enthusiasts—at least in Boston—was kranks. In any case, I can't find a viewable copy of the original picture that illustrates someone "lacing it out."
The two earliest matches in the Library of Congress's Chronicling America newspaper database for the verb lace in the context of baseball are from 1888. From "They Played Ball: Giants Won To-Day's Game from Indianapolis," in the New York Evening World (May 8, 1888):
Ward was sent to first on balls. Ewing went out on a foul tip. Ward went to third on Connor's safe drive over second, Connor getting to second on Denny's muff of the throw in. Slattery laced the ball over short for a base, bringing Ward home. On [Indianapolis catcher] Buckley's throw down to catch Slattery at second Connor scored[.] Slattery, was caught between second and third and run out. Two runs.
And from "Ah, Our Giants! Chicago Handsomely Defeated in the First Game," in the New York Evening World (May 10, 1888):
Pfeffer sent a hot grounder to Richardson and was retired at first. Big Ed Williamson was sent to first on balls. Burns laced a hot grounder to Richardson, who fumbled and threw to Ward, who muffed, Williamson landing safely at second and Burns on first.
It seems quite likely that these two instances, published two days apart in the same New York newspaper, were written by the same uncredited sportswriter. I didn't find any instances in Chronicling America search results that mention hitting a baseball "on the laces." If that phrase is the source of the idea of a batter "lacing" a baseball, it has yet to be substantiated by examples in print from 1888 or before.
As for the alternative argument, proposed in an answer by Fattie, that laced indicates something akin to "guided successfully through a series of twists and turns"—a meaning that would make perfect sense in describing someone weaving the ball through traffic on a British football pitch—it is not hard to find examples where laced is used in the context of home runs, which involve no weaving at all.
For example, from Bill Baer, 100 Things Phillies Fans Should Know & Do Before They Die (2012):
Thinking [Randy] Wolf would be taking again [with a count of three balls and no strikes], [Adam] Bernero grooved a batting practice fastball over the plate. Who could fault him? Ninety-nine percent of pitchers would be looking for a walk there. Wolf, representing the 1 percent, whipped the bat around and laced the ball over the right-field stands for his second home run of the game and the fourth of his career. The Phillies were up 9–4 and would go on to tack on six more runs for an easy 15–4 rout of the Rockies.
And from David Benham & Jason Benham, Miracle in Shreveport: A Memoir of Baseball, Fatherhood, and the Stadium That Launched a Dream (2018):
I know it's a crazy dream, but that is what I felt like at the plate. God's presence was so powerful when I was in the box that often after I laced the ball over the fence or delivered one of my many game-winning hits that year, I retreated behind the dugout to pray—and cry. I couldn't help it.
And from Ken LaZebnik, Buzzie and the Bull: A GM, a Clubhouse Favorite, and the Dodgers' 1965 Championship Season (2020):
The stadium clock showed that it was almost midnight when Lou Johnson came to bat. Red reliever Joey Jay threw, and Johnson laced the ball into the left field pavilion for a walk-off homer. The Dodgers had done it. They were now in first place.
I don't have any sources to prove it, but my understanding has always been that it is the shortening of a longer superlative statement "he knocked the ball right out of the laces" (alternately "he knocked the cover off the ball") which implies a force so hard that the laces holding the leather cover on are ripped apart, and only the inner core of the ball is launched.
I'm mystified by this question and the answers, and I'm mystified by the M-W definition.
To "lace" a situation means ... to lace it.
It can't really be defined any more than that; put a lace (say!) through a series of holes in which it belongs.
Either literally (with - say! - a lace) or literally with another object or of course metaphorically (as in politics, etc).
ie, you guided something (literally or metaphorically) successfully through a series of twists and turns.
It's very similar to saying "thread the needle". (Thread the needle, ie you "guided a largish object through a small hole".)
Obviously, it's hard to google many terms due to clutter (eg, the laces on footballs, skinhead slang, etc), but
There are innumerable both literal and metaphorical examples.
Taishi NARIKUNI laced his way to the 70kg world title ...
Cody Goodwin laced his way to a 10-0 technical fall, which is also a freestyle rule
Assylzhan Yessengeldi laced his way to the 61kg finals
He power laced his way to 3 points
My giant Maine Coon cat, King, laced his way through the legs of my lounge chair
lead guitarist Michael Wilton laced his way in and out of the spinning and howling guitar licks that augment the track's
Taylor laced his way to 40 off 32 balls, an innings that included five fours and two big sixes
The tall man laced his way through every couple on the dance floor
If you add almost any field of endeavour to the search (try words like horse, golf, sailing, politics, cars, child-rearing, cabbage, marriage, trees ... etc, etc, etc) you'll get innumerable examples.
Gonnella started fifth and methodically laced his way to third on lap eight
laced his way in and out of the stream of vehicles
Mr. Herriott held the reins of his spirited horses, and brought them down to a steady, rapid trot. It was a cold but sunny day in February, and as he laced his way in and out of the stream of vehicles...
His hands carefully laced his way through his bloodstained feathers
laced his way through the Yeomen forward wall for one long gain after another Quarterback Rich Poling added to the Crimsons defensive frustrations
Swooper ducked and laced his way through the net, knowing better than Anna what would happen if they touched one of its jagged strands of light
Bruntil, down 1-0, created her angle to an attack and laced her way to a tech
Metaphorical uses ...
the same Brad has laced his way throughout the teenage movie universe
Sarah HILDEBRANDT laced her way to a second world final.
