OK well first, a Pedersoli lock plate is for a Second Model, and is Waaay too small...and you'd be talking nearly $300 for that lock as well... with shipping.
IF...you can get the lock back...you can do as Chuck suggested and get the tumbler worked on to restore the half cock notch, OR repair/replace the sear, and be good to go.
The Rifle Shoppe offers a completed 1st Model 1756 LLP Lock for $295...and that
should be large enough to then fit it to your musket. HOWEVER..., you're probably talking about 24 months wait...call them and maybe you'll get lucky, and they have a finished lock on the shelf???
Loyalist Arms is offering under their
"specials" a 1728 musketoon kit. You'd end up with a lock that should be large enough to replace the lock that's missing. But that's a bit too much for a lock from India, when the Rifle Shoppe is offering a large enough lock for $295 + shipping, finished .
The other answer is to buy another LLP, from Loyalist Arms or Veteran Arms, while working on getting the lock back from Middlesex Village...then if you get the lock back, sell that now complete MVTC musket, or if you exhaust all options, sell the remaining bits of the MVTC gun, to help defray the cost of replacement.
LD