Take a look at the sentence again:
Kevin __________ the dripping barbecue sandwich on his plate and grabbed
a fork and knife. He ignored the stares of the other restaurant patrons
and ate his sandwich with utensils.
Kevin put the sandwich on the plate. Thus, you need a form of lay. Since the sentence is past tense, you need the simple past form. 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 |