On Facebook a retail business posted a $1 lottery ticket and stated will share with Friends. If the ticket really wins the $4 million is that binding?
Yes, for those who 'liked' the business after reading the post, but less likely for those who had already liked the business.
Under contract law, the business's post is an offer to share the winnings with anyone who is a friend of the business on Facebook. A promise is enforceable if consideration is provided under a bargain; the consideration can be of nominal value (e.g. the act of 'liking' a page).
In the context of a business page, in a time when 'followers' and the like are regarded as valuable from a marketing perspective, it is entirely reasonable to interpret the post as offering an exchange of likes for a chance to win money. The commercial context and involvement of money would cause a court to presume that there was an intention to create a legally-binding contract (Ermogenous v Greek Orthodox Community of SA Inc (2002) 209 CLR 95; Banque Brussels Lambert SA v Australian National Industries Ltd (1989) 21 NSWLR 502).
I am not entirely familiar with how the designation 'Friend' applies to businesses on Facebook. My understanding is that businesses have pages that are different to user pages. Businesses don't have 'friends'. They have people who 'like' the business. However, the word 'Friend' in the post has to be given content and therefore would be read as 'people who are listed as having liked this page'.
People who had already liked the page are less likely to be able to enforce the promise to share the winnings, because they didn't do anything. They might be able to argue that they forwent the opportunity to un-like the business and that this forbearance is consideration. However, they would have to show that this was in consideration of the offer to share the winnings.
Contract law is based on objective manifestations of agreement, not subjective thoughts (Taylor v Johnson (1983) 151 CLR 422), so it isn't necessary to show that the individual did in fact have the offer in mind when they liked (or didn't un-like) the page. However, it is necessary that the promisee have knowledge of the offer and not be acting out of some completely separate purpose (R v Clarke (1927) 40 CLR 227); therefore if a user had liked the page some time ago and never knew about the offer until after the lottery was won, then they might have a hard time claiming a binding contract.
Aside from contract law, the other possible head of liability is equitable estoppel (I mention this particularly for the people who had already 'liked' the business page before the offer was posted). However, equitable estoppel usually requires some element of detrimental reliance. Leaving a pre-existing 'like' on a page in reliance on a promise to share lottery winnings is unlikely to stir a court to find an equitable estoppel, since the detriment is trivial. Contrast Waltons Stores (Interstate) Ltd v Maher (1988) 164 CLR 387, where the detrimental reliance was knocking down a building and starting to construct a replacement. Equitable remedies are discretionary, so the judge has plenty of leeway to not order compensation.
This answer is based on the common law. There is nothing in Texas law which would make the outcome any different to the outcome in any other common law jurisdiction.