You mentioned the names Polly, Molly and India Mary earlier - are these the names of your daughters or merely ones you are considering along with Lola-Mary?
Lola-Mary is an odd combination, in my opinion: one very modern, one very traditional. It doesn't work for me and I don't think it flows particularly well either. Mary-Lola sounds better to my ear but I think it's still a very clunky combination. Not my style! Everyone I know with a hyphenated name is inevitably called only the first.
Go with Lola Mary Catherine (first name, two middle names) instead. I personally really like the other posters' suggestions of Marina and Mariella. The coil to which you referred is actually called the Mirena coil and I'd be surprised if many people were to make that connection. Certainly none of your daughter's classmates would!
I would use Marian/Marianne, Maribel, Maricela, Marie, Marielle, Mariella, Marina, Marcia or just plain Mary instead. There are some very pretty names related to Mary or with similar letters.
If you wish to pair Mary with another name to make a hyphenated first name, select something similar to it in style that flows well (e.g. Mary-Anne, Mary-Beth, Mary-Lou, Mary-Kate, etc.).