So far, I thought that 'Do you want to go out for lunch?' has exactly same meaning as 'How about going out for lunch?', as both sentences are giving suggestions.
However, I recently read that 'Do you want' sentence asks listener's simple wish or hope, while 'How about' or 'Why don't you' sentence is giving suggestions.
If that explanation is correct, then how can I distinguish each sentence's meaning? Or can I still use both sentences for giving suggestions?
You have it right, but the context tells all in the sentences that precede the the question.
If one night your grandmother says she wants to eat out more, the question of "Do you...lunch" is a general request for information, not an invitation. If at work it is time for lunch, then "Do you" and "How about" both mean the same suggestion, 'Let's go out now, shall we?'
Similarly at a dance, you are asking for a dance partner when you ask "Would you like to dance?" However, you are asking a general question when your grandmother says she want to get out more, and you ask "Would you like to dance? We could take you this weekend."
Depending upon the context, the sentence 'do you want to go out for lunch?' can be:
Do you like to have the lunch here, or want to go out for it?
If you would like to go out for lunch, you can come with me. I am going out.
We have lunch here ready, still do you want to go out for it?
'How about going out for lunch?' is definitely a sort of invitation or suggestion.
How about going out for lunch? Come on, let's go!
