Are there English minimal pairs created by different syllabification, specifically of lexical words?
You are asking after minimal pairs created through juncture, or the transition between two phonemes. Changing juncture would effectively change the syllabification of a word, since it would change whether adjacent sounds are part of the same syllable or are part of two adjacent syllables.
There are lots of examples of juncture generating minimal pair phrases. A generative one is to play with the articles a (before a consonant) and an (before a noun):
an aim / a name
an ad / a nad
an app / a nap
Notice how the /n/ changes slightly in emphasis between these examples but the vowel stays the same. The only difference is an allophonic change - the consonant /n/ is more voiced when it starts the word. Junctures are created through these allophonic changes.
The problem with finding a word-level minimal pair is suggested in this Wikipedia article on minimal pairs. English juncture produces semantic differences primarily between words, and those junctures are created by allophonic shifts, or subtle shifts in how we pronounce phonemes. Within words in English allophonic changes seldom present more than an accent difference. Imagine someone saying cat simple (/kæt/) versus with an aspirated t (/[kætʰ/) and having that produce a different word. It's just a cat that sounds funny! So if the allophonic sound differences don't generate new words, then syllabic breakdown within a single word doesn't generate another single word.
Finally, exceptions are hard to find because many near-homophones that seem to qualify (like catastrophe -> cat ass trophy) involve vowel shifts (from /kə/ to /kæ*/ or /ka*/ that make it no longer a minimal pair based on juncture alone. The "co-ring -> coring" example mentioned above also fits this paradigm: the /ko/ of "co-ring" is shifting to the /kɔ/ or /kə/ of "coring." So we're not just looking at a syllabic shift but a vowel shift. That said, the absence of evidence is not the evidence of absence, so it's theoretically possible two words could be juncture-based minimal pairs.
If you include compound words in your definition of "lexical word", this should be possible in theory, but I can't think of a specific actual example.
Here's a hypothetical example: you could have a pair like sauce.pan vs. "saw.span", where the first would tend to have a phonetically shorter vowel in the initial syllable, while the second would have a less aspirated plosive in the onset of the final syllable.
In John Wells' article on "Syllabification and allophony", he gives the near-minimal pair of selfish vs. shellfish, and argues that the first is self.ish while the second is shell.fish. Aside from the difference in the first consonant, I think that some people might argue that "selfish" is actually syllabified as "sel.fish" and that the difference in pronunciation relative to "shell.fish" is due to the absence of tertiary stress on the last syllable (e.g. ˈshellˌfish vs. ˈsel.fish). Wells doesn't think that tertiary stress is necessary, but other linguists do make use of the concept. That's why I think the clearest example would consist of a pair of compound words. Wells also mentions the near-minimal pair of "toe-strap" vs. "toast-rack".
Some theories have more restrictive rules about syllabification
Wells' conception of syllabification isn't universally accepted. In some theories, the rule of "maximizing the onset" of a syllable is treated as a generally applicable rule, even across morpheme boundaries in inflected words (such as planning, which some linguists would syllabify as /ˈplæ.nɪŋ/, despite the fact that it is a form of the word plan /plæn/).
In such theories, there are several possible ways to analyze the distinction between pairs like "coring" and "co-ring" mentioned by Chris H. (In some accents of American English, both of these words can be analyzed as having the vowel /o/ as the nucleus of the first syllable.)
The answers by user340953 and TaliesinMerlin mention the concept of "juncture", which is basically the idea that word (or morpheme) boundaries correspond to some kind of phonological entity. My impression is that this is not a very popular term/concept in more recent theories; user6726's answer to this Linguistics SE question says that "the concept has fallen into desuetude in linguistics over the past half century".
The concept that I've seen used more often in papers that I've come across that take the maximizing-onsets approach to syllabification is to appeal to a larger phonological unit than the syllable, the "foot". "Feet" are mostly related to stress; to simplify things, you can think of each stressed syllable in an English word as being the start of a "foot".
We could say that despite containing the same syllables, /ko/ and /rɪŋ/, "coring" and "co-ring" contrast because the second syllable of "co-ring" is (or at least was originally) a foot, but the second syllable of "coring" is not a foot. (The exact division of words into feet seems to be somewhat controversial; I'm not sure whether it would be more better to analyze "coring" from "core" as
(ko.rɪŋ), with a disyllabic Hσ foot, or as
(ko)rɪŋ, with a monosyllabic H foot followed by an unfooted syllable. Feet are commonly said to be "binary at some level of analysis" (either bimoraic or bisyllabic) which permits
(ko.rɪŋ), and I think that would be the more usual foot-based analysis, but I think some people may have proposed more restrictive definitions of feet.)
There are homonyms where one word is formed from a stem+prefix and the other isn't. The stress is often different, or the first/prefix vowel sound. One of the closest, at least in some accents, is coring (wiktionary). The more familiar meaning is from core+ing: "cutting a core" or (n) the core so formed, but there's a mathematical meaning from co+ring: "The dual of a ring".
I don't think it is possible in English, since, unless the actual phonemes themselves change, as discussed in other answers, then the words would be pronounced the same. This is because we tend to pronounce syllable boundaries according to the rules of phonotactics, not according to the morphemic boundaries.
So if nitrate, night rate and nigh trait were each one word, and if the phonemes themselves were the same in each case, then they would simply sound the same, despite three different morphemic boundaries:
where | represents the morphemic boundary.
I think we have to have to go to a language like Irish, which does something you don't see in English, to get two words that differ in morphemic boundary, but the problem is they sound the same!
This isn't quite what you are looking for but I think it is the nearest you will get.
Some words than historically ended in an -n now cause the following word to modify instead. This is usually called "eclipsis" but nasalisation is the correct term for the grammatical process, with "eclipsis" referring to the orthographic convention. It is described here. For anyone with Welsh (or similar) it is the nasal mutation with the addition of a rather strange orthography.
So from ár (treated as from *árn) "our" and athair "father", we get ár nathair /aːr nahǝr/ "our father". Unfortnately, nathair also means "snake", so ár nathair can also mean "our snake", thus confusing everyone who has ever learnt the Lord's prayer in Irish. Thus nathair is a pair of homonymous words, caused by a movement in the morphemic boundary.
They sound the same and look the same, unless you use capitals, as in the Lord's Prayer in Irish, in which case you get
Ár nAthair vs Ár Nathair
I know this is not exactly what was asked for but I don't think you will find anything better. Of course it is as much to with orthographic convention as anything else. This is illustrated by switching to Scots Gaelic, where we get
Ar n-Athair vs Ar Nathair.