There's a place in Falset called Quintana (or something like that). They serve vegetarian and non-v. They have a good reputation. I had lunch there once and it was on a par with other mid price restaurants. The family also owns and runs a health food shop.

I'm not really a good restaurant critic as I nearly always leave feeling mild disappointment, maybe because the really good meals I've had were so much better than the good ones.

I don't know where you are, but if you're in Tortosa, it's a bit of a hike to Falset.

Never heard of anywhere round here that was specifically vegetarian, of course the simple answer if they are non meal eaters is to eat on the coast, any decent restaurant in places like San Carles will serve mostly fish or seafood and so meat is nowhere to seen.  In San Carles try any in and around the port area, la Varadero is good if a little pricey.  The tourist menu is a good sample of local seafood fare.

Don't go to the expense of a meal out, most of the Spanish restaurants don't do things without meat or fish, cook your own see www.khanapakana.com/veggie/