Grammar

Yes you can! Examples:

I would like to eat lunch at 1 o'clock.
I will eat lunch with my friends today.
I want to eat lunch while watching TV.

But it is a lot more common to use "have" instead of "eat" in this context, for example:

I would like to have lunch at 1 o'clock
I will have lunch with my friends today.
I want to have lunch while watching TV.

It's possible also to say :
I would like to lunch.
I will lunch.
"lunch can be used as a verb".

everlastinghopeI would like to lunch. I will lunch.

I suppose these are not incorrect grammatically, but they are certainly not common. I don't think I've ever heard anyone say either one of these sentences.

khoffI suppose these are not incorrect grammatically, but they are certainly not common. I don't think I've ever heard anyone say either one of these sentences.

I've also never heard someone saying that but I know for sure that they're correct.
Why can't WE be the first ones saying that since it's correct !!!!

Most people who are learning English aspire to speak it the way it is commonly spoken, so I try to point out whenever something "correct" is not actually commonly used. Feel free to be innovative if you like!