Take a look at the sentence again:
Bill went to the bank interview smelling of wet dog. He had __________ his
one suit on the bed before going into the bathroom to shave. Dripping from
the rain, Skipper, his Labrador retriever, decided the jacket made a perfect
towel.
Bill put his one suit on the bed. Thus, you need a form of lay. Since the sentence has the auxiliary verb had, you need the past participle. Consult the table below or review the rules.
Infinitive | Definition | Simple Present | Simple Past | Past Participle | Present Participle |
to lay | to put something down | lay(s) | laid | laid | laying |
to lie | to rest or recline | lie(s) | lay | lain | lying |