I've owned and shot both a Lyman GPR flinter and a T-C Hawken flinter, and to me the locks are so similar as to be identical. Like many if not most flintlocks, they have preferences as to what kind of flint they prefer and how they like it clamped in the jaws of the cock. I prefer my T-C Hawken, but that's just me and the shape of the stock, both rifles are good, dependable arms. As to fit and finish, both are fine in the rifles I have.
As to historical accuracy, The Museum Of The Fur Trade in Chadron, NE states that as far as they know there is no extant example of a flintlock Hawken from the Hawken shop, nor is there mention of any in the Hawken records.
Your mileage, as always, may vary.
Three Hawks