Titles are possibly the hardest part of any project.
I don't have the time just yet to read it all, but I'm super excited to because I love Moulin Rouge. Especially now that there's a broadway version of it. (Amusingly, I've RP'ed Christian from that version quite a bit.......tho it's all a bit different from the movie).
There are as many ways of coming up with good titles as there are people who come up with titles for things. But the core thing tends to be identifying what is key to the story. IE in Moulin Rouge, it's named after the venue where it all takes place (and the reason the events are even happening). It could be named after the central character (Harry Potter, any superhero comic, etc). A general concept that ties the characters together (ie Les Miserables, meaning The Miserable Ones). A theme, and object, a concept, a color. Anything.
Basically, make a list of the things that are most important to the story as a whole. Mash them together in new ways. See what stands out. A lot of it at that point is going with your gut. Or in the end, just deciding one is "good enough."
As for "Laces and Lies"...I'm not sure. It makes me think shoe laces. If you mean like frilly lace, you could play around with that. Keep it tied to the original title with "Red Lace" or another luxury fabric, "Lies in Velvet." Which is also a play on words. Lying and laying.
For example: my comic is called River City. It describes where the story takes place, and is also an incredibly common nickname for a large city (since most of them are by or around rivers). So it implies it could be in any city. (It was also just what I called the city itself before I had to give it the proper name of New Castor).