Should I hide the fact that I did a group assignment completely by myself?
Personally I would dodge the issue using


  Most of the work is done, but we need to...


I don't think it will really matter which option you go with, but that way you don't have to worry about it.

Anyone setting a group project knows that it is fairly likely someone will end up doing all the work. If they don't take any action to avoid that (and it sound's like they haven't in this case), then presumably they don't really care.

I understand that you want to get the credit for doing the work. But I agree it might come across as tactless to point out the situation in your email. It might be more productive to separately have a conversation with the lecturer about why they haven't taken steps to avoid the situation occurring.