This is very colloquial, at best, if not downright incorrect. However, it is currently in use, as shows this ngram.
(Following copy of ngram mentioned above added as a later addition to make up for user psmears' problem)
Syntactically, this construction is not analysable. It means "I'll tell you what we'll do.", which is used much more often: ngram.
The illogicality comes from the fact that a nominal clause must be replaceable by a noun phrase: it is the object of "tell", and therefore must represent a thing, whether a concrete thing or an abstract one; instead of a verb form telling what action is performed on the object "what" (in "what let's do") there is an order. That is not possible.
(Following reference below is a later addition to make up for user psmears' problem)
(ref. 2020) “Now let's talk about 'clean,' son. Clean means no messes around—no paper, strings, bones, sticks, or anything that messes up the place. I'll tell you what let's do. Let's just clean up half the yard right now and look at the difference.
This final addition of references below are just a few of those that can be collected.
(ref. 1, 1999) MISS NORTHERN : I seen them two or three times . Don't look at the feet . Let's don't look at the feet . JUDGE TODD : I tell you what let's do . MISS NORTHERN : Don't look at the feet . JUDGE TODD : Let's don't look at the feet .
(ref. 2, 1960) Good boy ! Now you've got them . Now we GO ! Still not enough gas ? Boy , how ough can it get . It's enough to make an ambitious guy discouraged . Tell you what let's do . Lower the density altitude and save a little gas that way
(ref. 3, 1965) Tell you what let's do . Let's clean off a nice leaf of that giant sagittaria . Then you lay a big batch of eggs .
(ref. 4, 1931) ( Synge , The Well of the Saints , Act III ) . The let - form often occurs in a substantive relative clause : ' Ah'll ( I'll ) tell you what let's do , Miss Leighton ! ' ( W. D. Howells , A Hazard of New Fortunes , II , Ch . II ) . ' I tell you what let's do : let's all run
(ref. 5, 1940) But if you feel that way about it , I tell you what let's do . I was going over today to the new chute we're putting in on Forty .
(ref. 6, 1997) I went over to the ones that were in the union and I said , “ Look , Eli needs that letter so I'll tell you what let's do . I'll memorize the first two lines of it and go in the bathroom and write it down .
(ref. 7, 1931) I'll tell you what let's do . Let's divide this one . I'll dance the first half with you , Robert , and the other half with you , Richard .
(ref. 8, 1985) I'll tell you what let's do . I would like for you to write me something , anything , about a time when you had a romantic attitude . You were really expecting something to be great ,
(ref. 9, 2011) Look , I tell you what let's do . I've got an idea . ” An hour later , mid - afternoon , the five of them were at a beach near Palmilla , just south of Ashley's favorite beach bar . The sky was a cloudless cerulean and the surf impressive .
(ref. 10, 1961) “Just look at your hair—all mussed up. I'll tell you what let's do. Let's cut it off! I'll do it for you—now, right now