Lamentably means in a very unsatisfactory or disappointing way. You can put it on a verb (“they performed lamentably”) or out in front of a whole fact (“Lamentably, few people came”). It is the adverb of lamentable, and it has the same formal, slightly grave tone. Though actually, like the adjective, it sits between “sadly” and “badly”: sometimes you mean you regret the fact, and sometimes you mean the quality was poor. Everyday English more often says sadly, unfortunately, or badly. Use lamentably when you want that heavier, written feel.