There are different types of vegetarians.
And there are some that proclaim their vegetarianism, but would not be considered as such by others.
Best ..... to outright ask your neighbours!
Tell them you would like to invite them for dinner, and want to respect their choices.
Ask for their help in planning the meal. Perhaps even sharing of recipes.
You may find that what they eat really is no different foods
than you would eat (along with their exclusions).
You may also find that there are foods they would suggest, that you have never tried before.
What others advise you here, may or may not hit the mark.
Being neighbourly friends, already, should make it easy to open the door to this discussion.