That's an interesting datum about the Codex Sinaiticus. There are a few other unusual things about this saying. It appears only in the Greek version of Thomas 36:2-3 (P. Oxy 655) and not in the Coptic version. The Lukan wording is also slightly different. If we compare the two side by side, with the critical reconstruction of Q and the Greek version in Thomas, the differences are quite apparent:
Matthew 6:28: katamathete ta krina tou agrou pós auxanousin ou kopiósin oude néthousin ("Observe the lilies of the field, how they grow, not they toil nor they spin").
Luke 12:27: katanoésate ta krina pós auxanei ou kopia oude néthei ("Consider the lilies, how they are growing, not toiling nor spinning").
*Q 12:27: kata[[mathe]]te ta krina pos auxan[[ei]], ou kopi[[a]] oude neth[[ei]] ("[[Observe]] the lilies, how they are growing, not toiling nor spinning").
Thomas 36:2: [pol]ló krei[sson]es e[ste] tón [kri]nón, hati[na o]u xa[i]nei oude n[éth]ei ("[You are] far better than the [lil]ies which are not carding nor spinning").
The differences between Matthew and Luke are pretty slight -- a different imperative verb with didactic force, the addition of "of the field" in Matthew, and the different tense forms for the verbs "grow", "toil," and "spin". The Thomas saying on the other hand is much different. There is no didactic verb of learning from nature; instead there is an explicit comparison between the lilies and people. There are also only two verbs associated with the lilies; "grow" is not represented entirely, and "card" is in the negative phrase instead of "toil". The interesting phonetic resemblance that PP draws attention to is between ou xainei "not carding" in Thomas 36:2 and auxanei in Q/Luke 12:27. Since Thomas and Q are related indirectly to each other by drawing on similar oral traditions, it is possible that the phonetic confusion occurred in the oral stage, with alternate versions of the same saying existing side-by-side. At the same time, the graphemic similarity could have also contributed to later scibal errors -- as PP suggested. It is possible, for instance, that the difference between Q and Thomas reflects a phonetic confusion in the oral stage while the Codex Sinaiticus error reflects a later graphemic confusion, or as PP suggests, influence from the Thomas version of the saying.
I really don't know however which version might be more original than the other, tho Dale Alison might provide a clue by examining the sources lying behind the logion. Q 12:27-28 directly compares the lilies with "the glory of Solomon" (cf. doxa "glory" of Solomon in 1 Chronicles 29:25, 2 Chronicles 1:12 (LXX), Josephus, Antiquities 8.190, Testament of Solomon 5:5, etc.), whereas Thomas makes no such application. It is possible that the saying originally circulated as a sapiental proverb but the Q version is quite intelligible in light of the Solomonic tradition which clearly has been used in this passage. Note especially how the lesson from nature in Q 12:22-31 is modeled on that of Proverbs 6:6-11, with the same moral in each: "Be diligent, and poverty will flee from you" (Proverbs 6:9-11), "Seek the kingdom, and you need not worry about food or drink or clothing" (Q 12:29-31). The specific example of the lilies is not found in Proverbs, but it has close connections with the Solomonic tradition. Alison points out that over half of the 22 occurences of krinon "lily" in the LXX are associated with Solomon and the writings attributed to him, especially Canticles 2:1 which refers to Solomon as "a lily of the valleys", whose lips are like lilies (5:13), who "pastures his flock among the lilies (2:16, 6:3), etc. Thus the Solomonic comparison in the logion is one that is found in the OT. This has implications for the verbs associated with the "lilies" in Q 12:27 and Thomas: "grow," "toil," "card," and "spin". Of these, kopiósin "toil" is firmly in the Solomonic tradition. The word occurs in works attributed to Solomon (cf. Psalm 126:1 (LXX); Proverbs 4:12 (LXX); Wisdom 3:11, 9:10, 10:10; Testament of Solomon 2:8, 10:10), and is especially prominent as one of the main themes of Ecclesiastes: "What do people gain from all the toil (kopiaó in some LXX versions, Aquila, and Symmachus in Ecclesiastes 2:24, 4:6; mokhthein in other versions of the LXX) at which they toil under the sun ... I hated the whole of my labor with which I toiled under the sun" (Ecclesiastes 1:3, 2:18). Solomon complains about his toil being to no avail, which is a contrast in Q to the lilies which do not toil. This would suggest that kopia is original to the Q version of the saying and interestingly Thomas, which lacks the Solomonic theme, also lacks this word.
This is pure speculation but I could imagine the following process of development: (1) We start out with a sapiential saying which compares the wise or the believers with the lilies. The agricultural metaphor here is most overt, with "spinning" and "carding" being the kind of labor that the lilies don't have to perform. It is this oral saying that is adapted in Thomas to the community of believers. (2) The author of Q draws together a number of these sayings into a short discourse on divine providence and the uselessness of anxiety over work and clothing and imitates the sapiential form in Proverbs 6:6-11, traditionally ascribed to Solomon. In Q 12:27-28 the examples from nature are directly compare with "the glory of Solomon," which is facilitated by the traditional likening of Solomon to lilies and Solomon's traditional anxiety and despair over "toil" in Ecclesiastes. The saying about lilies is adapted in this way: (2a) First, the Q saying needed a verb of what the lilies actually do, for this is what is found in the model in Proverbs 6:6-11, which instructs the reader to learn from how the ant "prepares its food" and how the bee "works earnestly". Lilies don't do anything other than "grow," so this is the verb (auxanei) that occurs in Q 12:27. (2b) Because of the phonetic similarity between auxanei and the ou xainei in the Thomasan version, it is possible that the author of Q drew on a version of the saying which already described the lilies "growing". In either case, the replacement of ou xainei with auxanei in Q deleted the reference to "carding" and also obliterated the initial negative in the ou ... oude construction. This meant that auxanei needed to be followed by a clause with a restored ou "not" and a new verb to fill out the ou ... oude pair. Thus, kopiaó was recruited from the Solomonic tradition (as suggested especially by Eccelsiastes 1:3, 2:18), with links possibly to the bee that "works (ergasian) earnestly" in Proverbs 6:8 (LXX). This preserves a verbal pair for the ou ... oude construction; Thomas has "not carding nor spinning," Q has "not toiling nor spinning". (3) Then the Q saying in Matthew was altered by the copyist of the Codex Sinaiticus to partly resemble the pre-Q version, either through recourse to alternate oral or written versions of the same saying or through a copyist error. I don't know what to make of the Codex Sinaiticus having "toil" and "spin" in reverse order.