This is very tricky as it involves two separate but very closely related verbs, to lay and to lie, that share a common form—i.e. lay is both the present tense form of to lay and the past tense form of to lie.
The primary difference between to lay and to lie is that to lay is transitive, meaning it takes a direct object, while to lie is intransitive and does not take an object. The verbs have the following forms: to lay—lay (present tense), laid (past tense), laid (past participle), and laying (present participle); and to lie—lie (present tense), lay (past tense),lain (past participle), and lying (present participle).
So using that information, given that all three are in the simple past tense, I can tell that number one is laid, which has the direct object of a hand, and numbers two and three are lay, which have no object.
Here's where you may be getting tripped up: laid is a form of to lay, and lay, in the simple past, is a form of to lie. In other words, the word lay in numbers two and three is not connected to the verb to lay.
As long as you know what tense the examples are in, it's simply a matter of whether or not the verb has a direct object.