No, the word "обедать" is a verb meaning "to have/eat lunch/ (dinner; though not used in Duo this way)". The same thing also happens with "завтракать/позавтракать" and If you know some German it's "frühstücken". xD
EDIT: Sorry for the confusion caused. When i said "frühstücken', I meant 'to have breakfast'. If you wanna say 'to have lunch', it's 'zu Mittag essen'. Haha, sorry for the German, this is supposed to be a Russian course.
Interesting. My sister (from Maryland and then Kansas) got into a huge misunderstanding with her boyfriend from Arkansas (a State very close to Kansas) about what time they were going to eat. She invited him to her house for "dinner". She meant for a meal in the evening. He said he couldn't make it. She asked why. He said because he had to work. She knew he worked the day-shift, so she asked why he was working over-time. It went on for about 30 minutes, both being really confused and getting a little angry, until they figured out that "dinner" for him was a mid-day meal, and "supper" was the evening meal. "Dinner"and "supper" for my sister were both evening meals - except on Sunday, when "dinner" means a large mid-day meal - but it's "Sunday dinner". "Dinner" on Sunday means an evening meal on Sunday evening.
As I've always seen it, "dinner" is your main meal of the day. Traditionally this always used to be the midday meal, so the expression stuck in some places, even as eating habits changed.
My mother tells an anecdote where she invited a friend over for "supper", meaning an evening meal, and she turned up very late expecting a small snack before bedtime.
just to make things possibly a bit clearer.
to have breakfast -- завтракать ("позавтракать" being the perfective aspect). to have lunch -- обедать ("пообедать"/"отобедать"(the latter would sound a bit old-fashioned or posh) are perfective aspects). to have dinner/supper -- ужинать ("поужинать" is the perfective aspect). to have a snack -- перекусывать. here be careful, because the word also means to bite through.
the respective nouns are: завтрак (m) -- breakfast; обед (m) -- lunch; ужин (m) -- dinner/supper; перекус (m) -- having-a-snack.
No...the listener would know what you meant, but it's not something English-speakers say. "Do you want to have some lunch," perhaps would be used, if the intent were to grab a quick bite of whatever food is available and then return to the activity at hand; but as "lunch" could be considered a mass noun the "a" would not be attached. The only contexts I could think of which might include "a" would be either an event ("There's a lunch at the conference center today,") or a situation in which a single meal for one person is specified, e.g., "I'm going to pack a lunch."