
You could try DNA testing..... but not via the usual route (which is highly inaccurate anyway).
Test are now available overseas for various colour genes, so you could ask for a test for a(w) and a(t) (which I suspect are the main colour genes your dog has). It if comes back she is a(w)a(t) then the initial guess of Husky x Rottie is more or less correct - inasmuch as she has a wolf-grey gene and is carrying black-and-tan....
Alternatively, with the mind boggling, that combination of genes could include Vallhund x Dobermann, Elkhound x Bernese Mountain Dog, Keeshond x B&T Dachshund, or Sable GSD x Lancashire Heeler....lol... but you would have narrowed the parents down to two very breed-specific colour genes, you wouldn't know which two.... but you'd have a better idea. Especially once Lola is adult and has matured into her final body shape.
Incidentally I have a suspicion that these DNA tests for crosses work on colour genes anyway. I recall seeing a YouTube vid of the woman in the USA with a purebred show Champion Am Staff, (black bicolour) whose results came back as Border Collie!! A couple of other results I've heard of came back as having Australian Shepherd as one of the crosses involved, which is so unlikely in the UK, I wonder if they threw that in to cover tricolour.