How to convert Proteus PCB design (ARES .LYT) to Altium Designer (.PCB)?
I checked the available file importers for Altium and I don't see ARES or .LYT listed. Even if there were such an importer available, you would need an Altium license to be able to use it.

However, there are many many pcb fab shops available, and 90% (or more) of them accept either gerber files or ODB++ rather than design files for any particular design tool. And 90% (or more) of the design tools can produce one or both of these formats.

Gerber is the older and simpler format. But it does need some external documentation like the units (inches or mm) used, and requires more manual handling by the fab shop. ODB++ is more modern and allows more automated handling by the fab hsop, but not all tools seem to have complete support for it yet.

If your tool can't produce either gerber or ODB++ then it's time to start learning a new tool.

If your vendor won't accept gerber or ODB++, it's time to start looking for another vendor.