Cartridge (other than Rega) with Rega RP10

If you know the mass of the arm then you can easily find compatible cartridge, just make sure the dynamic compliance of the cartridge measured at 10Hz and don't forget the mass of the cartridge and screws. Here is the article. I think it must be mid compliance and most likely the arm is mid mass. 

Is there a Lyra "house" sound?

A good MC cartridge must be absolutely neutral. Personally i have a phobia about cartridges with unprotected cantilever (like Lyra), it is so easy to bent!

@ladok this is one of the reason no one can tell you which cartridge is the best for your setup if another user setup is different, right? 

As for the neutrality of the cartridges it must be compared to the master tape during disc mastering process. These guys did it, read it. 

Lyra is very expensive cartridge, it depends how far you can go ... 

Dynavector KARAT 17D2 or next models with short Diamond Cantilever could be a good choice for less money. 

Dynavector with short Diamond cantilever is great and this cantilever is very well protected, the other two cartridges with long cantilever in front of the cartridge can be smashed easily and it will be a tragedy. 

17DX
17D2 mkII 
Delos 
Apheta 3