Yeah, the hallmark of P-W is uncontrollable and never satisfied hunger + some pretty profound intellectual disabilities.
Lucas seems to eat a lot mostly as a self comfort thing. Not super uncommon, it's very, very common among unmedicated mentally ill people. They feel shitty, eating makes them feel temporarily less shitty, defective head meat goes with, "EATING CURES US!" and it quickly can turn into a straight up binge eating disorder or addiction to food/eating.
And, after awhile, they need to eat more and more at a time to feel temporarily less shitty, and you get...y'know, pretty fat pretty fast.
Doesn't help that high sugar, high salt, high fat food is best and cheapest at tripping the "temporarily less shitty" feeling, at least, while they're actively eating.
A lot of people equate food with an expression of love or welcome and he takes that to a weird autism special interest level as well (i.e the "look at how good I cook! Look at how kind I am, giving so much food away!" shit).
He definitely eats as a form of self comfort, an attempt to show off his perceived suitability as a mate, and when he orders overpriced mediocre restaurant food, a show of what he thinks is wealth and his ability to be a provider.