ترجمة - إسبانيّ -انجليزي - Te extiendo una invitacion cordial a comer o...

"to eat or to dine" means lunch or dinner?

That's what I'll like to know. Does "a comer o cenar" refers to "either lunch or dinner"?

Comer in Spanish means both "to eat" and "to have lunch", but since at dinner too one is supposed to eat...it's lunch here.
"Si gustas" is not just please, literally is "if you like" (the idea).