Inside of lock showing sear spring.
From what I can see, yours does not have this sear spring located where mine is, also your gun looks like it was made without a safety.
The butt plate showing Trap Gun at the bottom was an advertising ploy to show these guns were good at the Traps as well as in the Fields.
I cannot find on our Members Only site the patent date to tell you what that was for but I believe it was for the "J" spring that holds the fore arm on.
Back in 1886 this gun was selling for $80.00
From the looks of your gun it needs a good cleaning in and out, and if you are not familiar with taking one apart I would have a reputable gunsmith that KNOWS L.C. Smiths do it.
Good luck with your fine gun.