It seems like the Lancaster towels are just 1200 GSM microfiber towels like these with a hanging ring. I don't have a Lancaster towel so I can't say for sure but they most likely are very similar.
If you want a towel from a shaving brand, I recommend Muhle cotton towels. No hype, good price, and great quality. They have a hanging lace too and the package comes with 2 towels.
I rotate between Muhles and some no-brand Turkish cotton hand towels, depending on our house’s laundry schedule. I mean, they are just that, nice cotton towels.