While staying overnight at Lily's house, Martin indicates that he would like to buy her car. Lily says she'll think it over. The next day Martin finds a note on the kitchen counter from Lily that reads, "I might be able to sell the car for about $22,000." Martin writes her a check for $22,000, takes the car keys off the hook by the front door and drives off in the car. Have Lily and Martin formed a binding contract?

Contract: It is a legal agreement between the two parties in which the two parties are equally responsible for their performance . In this, the offer and acceptance are necessary, so without these the contract become invalid.

From the law point of view,

Contract = Agreement + Enforceability

In the given situation, there is no legal contract between them which have no validity. So, they both are not bonded with each other.

It is a bargaining offer, not a contract offer.