Yes, it is right. :)

In spoken American English, you might he people say this. However, grammatically speaking, I don't think it's 100 percent correct. Tony above explained it well, and I think the simplest correction might be "He lost more money than I did."

There is apparently a longstanding debate in grammar about whether to consider "than" a conjunction or a preposition. Informally, people do say "He lost more money than me" with the idea that 'than' is a preposition. Others will say "He lost more money than I did" or "he lost more money than I lost" in which case you are comparing two phrases which each have a subject and a verb.