If you apply the words 'character' or 'personality' to a building you first need to understand that this is personification, so the fundamental logic behind this is that we can think of things as having qualities that we would normally apply only to humans. In the same way that we generally use these words to describe a person in a positive way, they are also usually positive attributes for a building. Some people might like a building and say it has character. It is possible that other people might not like it, but accept it has character. At the very least if you say a building has character/personality you are saying that you consider it to be unique or special in some way. Therefore these two words convey a concept. A 'feature' is a more factual quality (not a personal preference or a concept). For example it has a spiral staircase or large glass windows, etc. 'Feature' is a countable noun. So from a grammar perspective you would need to change your example sentence to say "... lack features." But, although this is grammatically correct, it wouldn't make much sense. You might say something like "...lack interesting features" , but you might have to be more specific and clarify what you mean.

In your example, "character" and "personality" are interchangeable. "Feature" doesn't work, but you could say "distinguishing features" and convey a similar meaning.