Not sure what rifle Lyman makes that is a perfect replica of one of J&S Hawken's products; I own two Lyman Great Plains Rifles and neither is a replica of a Hawken. They are very good examples of a typical 1870's plains rifle, but they are not by any means a true Hawken replica.
I also own T/C Hawkens; I think most of the purists are not so much unhappy with them as a rifle (for they are excellent black powder rifles) as they are with the fact that Thompson Center used the name Hawken to identify it. I suspect they'd agree it's a good, even fine, rifle, but it shouldn't carry the name Hawken.
If one really wants a true Hawken replica, contact the custom rifle builder Don Stith at the St. Louis Plains Rifle Co (
http://www.donstith.com/). He's the only source I know of for that genre.