"look forward to doing something" is correct, if you say "look forward to do something" people can understand you but it's incorrect because "to" in this phrase is not a preposition for making an infinitive, it belongs to the phrase itself. for example in "nice to meet you", "to" doesn't belong to "nice" but you add it for making an infinitive.
you can say "I'm really looking forward to this weekend", it proves that the "to" in this phrase belongs to the whole phrase. so you can't say "look forward to do something"