I don't see an L or an H, but under the thumb rest is a serial number: 0537.
 

It's probably ok, the convention of L and H marking was dropped after high pitch horns were discontinued.  How about the toneholes?  Are they soldered on or drawn out from the body?

I'm not sure what I'm looking at; I took a few pics that may answer your question about toneholes.

It looks like a Holton, probably from the 1930s or 40s.  The toneholes are formed out of the same piece of metal as the body.  If they were soldered-on rings, my call would have been Couturiere, who also supplied stencil brands and even some horns under the Holton brand.

http://www.saxpics.com/?v=gal&a=5170
 
The good news is that the horn is in your hands for the right price, it doesn't look damaged, and it doesn't have the nonsensical keywork that earlier Holtons had. The bad news is that Holton stencils are mediocre horns without much value.  Any repair bill over somewhere around $150 could exceed the value of the horn.  It's worth keeping in basic playing condition for a beginner, but as you develop as a player you'll probably want to move on.

If you need a replacement touch for the front F key, make one out of epoxy.

 

Thank you so much for your assistance.  Without your kind help, I know I could not have found this information anywhere else or so readily.  I appreciate how you presented the details in a clear and succinct manner.  

I think I will enjoy playing this, once I get used to the size and weight, and I'm glad to know I won't be in danger of harming anything of great value.


Thank you.


Sincerely,
Cindy