As a Hindu vegetarian having grown up my whole life in New Zealand, I would not be offended by someone at work suggesting a lunch/dinner place that served a lot of meat (I suppose this includes Beef as well). Sometimes I feel a little awkward and like I'm a bit of a nuisance because of my dietary requirements which sometimes restrict the variety of restaurants/cuisines we can go to.
From my perspective, the best thing would be for you to suggest a couple of places that do have sufficient vegetarian options and as mentioned above BBQ restaurants are not necessarily ideal. Most restaurants and cuisines apart from a few South-East Asian cuisines will have ample vegetarian options.
On the note of offending, I don't think you should be worried about offending them, as it is not rude to enquire about another culture. But do make it clear from what perspective you're asking e.g. "We want to go for dinner tomorrow night, does anyone have any suggestions.. oh and are there any vegetarians or dietary requirements?" The alternative when you're in a more curious mood, is to ask one-on-one "So are you vegetarian? Are many Indians vegetarian? What's the story with beef... " so on and so on.
Hope this makes some progress towards answering your question.