Two verbs: lie, lay, lain ... and ... lay, laid, laid.
The first is used is intransitive and is used of one's self.
The second is transitive and is used with an object.
She lay down | She lay on the floor -- past tense.
She laid it down | She laid it on the floor - past tense.
She had lain down | She had lain on the floor -- past perfect tense.
She had laid it down | She had laid it on the floor - past perfect tense.
Thus, "She lay the gift basket ..." is incorrect in any context.
And, "She had laid the gift basket ..." is correct only in reference to another action, which this preceded.
The ordinary usage, in describing what happened, would be to say, "She laid the gift basket on the coffee table."
To complicate all this, there is another verb, "lay," which is American slang I won't go into.