Take a look at the sentence again:
Saxe, Diane's horse, will let you know when she deserves another carrot
or apple. She sticks out her tongue so that it __________ outside her mouth
like a long, fat, pink worm.
Saxe's tongue rests outside her mouth. Thus, you need a form of lie. Since the sentence is present tense, you need the simple present 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 |