Take a look at the sentence again:
Pumpkin, my oldest cat, loves __________ on my pillow. All night long, she
and my head fight for room.
Pumpkin loves to rest on the pillow. Thus, you need a form of lie. The sentence requires an infinitive. 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 |