I don't think
Lydia Mary is a tongue twister at all! That would be my choice, it's beautiful.
Mary Charlotte is very cute, and
Mary is perhaps not common anymore, but it does have a "conservative" connotation to it nowadays, I'd say. At least for me. If I was to pick
Mary as a name, I'd pair it with a much more outrageous middle, to temper the plain/outdatedness - maybe
Charlotte could be swapped out for something with more.... zing? I don't know what your taste is, though.
But I will say that a beautiful
Mary combo has a lot going for it.
Mary has some impact now, because it's not popular anymore. A few years back some people I knew named their daughter
Mary Isabel and that name stunned me with its beauty and how unexpected it was. Something like
Mary Juliet or even
Mary Lydia would be incredibly beautiful.