I'm not familiar with the Lyman Deerstalker, but I don't see why not. It will just have to be inletted. Davis makes nice double set triggers. Are you familiar with inletting? It's really not hard, justs takes time. You'll need some transfer color. It's a film thats applied to the part to see where the part makes contact where you can't see. Some people buy Jarrows inletting black( it's a bit on the greasy side) others will hold the part over a candle or kerosene lamp, and let the soot collect on the part from a candle or kerosens lamp, some will use cheap lipstick. Just apply the stuff to the part and just position the part where you want it, give it a tap, remove the part, and remove the colored parts of the wood from the transfer color. You want to inlet the plate first, so remove the parts. Remove the front return spring,then the main trip spring. Use a 1/16 pin punch to tap out the pivot pins. Put these parts in a CONTAINER with a LID for two reasons, one to keep from getting other bench debris mixed in with it, two so they don't get kncked over and lost. Once you get the horns of the trigger plate inletted, the plate should be down to the surface of the stock. I HAVE TO BACK UP A BIT. You have to prepare the part for inletting.You file a slight bevel on the back side of the plate on the edges that are the front and rear extensions of the plate, this allows the knife to trace along the edges with out taking up the room for the thickness of the blade.That's sides , rear and front only. NOT THE HUMPS IN THE CENTER! Thats where the shoulder groove for the front return spring rides(I know this because my first one, I filed it almost all off, had to get a new plate).
Also I might add Before you buy a trigger... You have to measure with a depth guage from the stock to the sear bar. see if the tripped trigger will reach. JIM CHAMBERS sell a davis trigger with a higher trip bar about 3/16 than the DAVIS triggers. Just make sure it's going to reach. The other thing is you probably have to bend the rear of the trigger plate to conform to the shape of the stock. When you're pretty much all inletted, flush with the surface of the stock. you'll have to make a judgment call as to its depth, so long as the trigger fits and works. then file the plate down flush, take it out polish it up , drill the rear screw hole. I did forget to mention the front tang screw....
... You have to make sure it's not going to interfear with the trigger. The trigger plate comes pretty long, and I usually have to trim it down 1/4 to 3/8 of an inch. But you'll have to lay this all out.If all goes the way it's suppose to with the trigger plate in you'll be able to drill the tang bolt. It might be a metric thread. Just make sure you use a tap drill for that size screw. After the hole is drilled, tap it through the tang into the plate. If you cant tap it all the way thru, take the tap out, the plate out and and finish tapping the hole.
IT'S REALLY NOT THAT HARD..... JUST TIME CONSUMING.....
GOOD LUCK.......George F.