NOT A TEACHER.
No, only "Let's go eat" is correct.
... but not for users of standard British English, who would say 'Let's go and eat'.
The -ing form would be OK if you were referring to an activity: 'let's go fishing/sailing/swimming...', so perhaps the rule is '...an activity that involves locomotion'. Just sitting at a table eating doesn't count! Perhaps some other teacher can express this better...
b
Are you suggesting that "Let's go eat" is poor grammar?
I agree with Bob. It's not normal for non-American English.Are you suggesting that "Let's go eat" is poor grammar?
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