RE: lyman frizzen....
I would have to have the lock and the two frizzens in front of my face to answer your question. In all probability, the two are not really interchangeable. Maybe the Lyman will work, maybe not. But if sparking is the problem, you can have the TC frizzen "half-soled" with a piece of file steel, or just re-heat-treat it to make it harder so it sparks better.
(You may have to reshape the spring, or make a new one. The spring is supposed to hold the frizzen good and SHUT before the flint strikes it, so good sparks are produced, then help snap it OPEN and hold it open when the frizzen is pushed forward by the flint so the sparks will not be impeded as they fall onto the priming charge. Consequently, the spring must have good, solid contact with the frizzen projections at both positions, open and closed!!)
"Bitte, trinks du das Wasser nicht. Dahin haben die Kuhen gesheissen."