You seem to be asking several different questions. It's all very jumbled and it's hard to know what exactly you are asking about, because
there is no precise context, yet again
! 
Please think very clearly what you are asking and
give us context.
"Let's ..." is a way of suggesting an activity. "Let's" is an idiom. It's short for 'Let us' but 'us/'s' is
never replaced by another pronoun.
"Let's have/do a barbecue!"
"Let's do some grilling!" does not mean the same as "Let's have a barbecue". I have no idea what it means or who would say it. A barbecue
is a sort of 'grilling' in British English.
"I will" is a way of saying what you intend to do, or make an offer.
"I'll grill/do the vegetables, if you grill/do the meat"
"We'll have a barbecue!" is a way of saying
you have decided what you and everybody's going to do.
A barbecue usually involves grilling meat
and vegetables. Why talk about vegetables as a separate thing?
Unlike some people, I'm not worried about using 'do' in this context.
It's used whenever people are deciding who is going to prepare specific items for a meal to which everybody contributes.
"I'll bring/do a dessert."
"Mary's bringing/doing a salad."
Or if people are sharing the various preparation tasks.
"I'll peel/do the potatoes."
"I'll make/do the sauces."
(Somebody else who doesn't 'do' barbecues!

)