Tex; The basic action of the Lightning rifle had very little leverage,compared to the lever actions as far as ejecting.
You did NOT say what you are shooting in it. Reloads?? These rifles tend to have difficulty,unless the brass is perfectly sized.
I would segregate cases,if you have a 44/40 revolver and use them separately. Next,check the rim diameters and thickness IF you are using different brands of cases.
And of course,do follow the previous posters advice about working the action correctly.
I am assuming that the chamber is not rough and that the extractor is in fine shape.
These are great old guns,but even when they were new,this was a problem,especially with reloaded brass. I had a 38/40,for a while,but traded it off to a cowboy action shooter,because I never dared push its velocity,with loads that I don't hesitate to fire out of some Colt revolvers,in the 1900-1930 time frame. Once I gave the Lightning a good cleaning,polished the chamber and used only R-P brass for the rifle only,it worked fine.
Interestingly,a Remington 14 1/2 pump rifle in 44/40,never had any feed or ejector problems. Of course,it was a newer design! Only long gun I ever regret trading off.
Hope this helps,
Bud