For some reason the only version of Tomb Raider 1 available on GOG is the one that uses an outdated, discontinued branch of DOSBOX (yhkwong version) along with nGlide. This way was maybe the best about 10 or so years ago, but now there are much better alternatives that allow TR1 to be run natively on Windows, with much better performance and quality.

Because of that I strongly suggest to update TR1 with one of these patches:

https://www.tombraiderforums.com/showthread.php?t=225845 - tomb1main
https://www.glidos.net/tombati.html - tombati
https://github.com/ata4/glrage - GLRage wrapper by Barracuda

Both tomb1main and TombATI are based on GLRage by Barracuda. Tomb1main is the newest one and it is constantly updated. TombATI is not updated anymore, but it works well. GLRage wrapper isn't updated either but it works great too. All of these patches allow you to play Tomb Raider 1 natively on Windows. It's because they are based on old executable made for ATI 3D Rage cards, which was the only one made strictly for Windows.

well the only problem i have with the older games is keyboard pc controls. Really if you don't have a joystick its almost unplayable with the bad controls, bad keymapping. Trying to move about with arrow keys or asdf or what ever is just unplayable compared to using a joystick as its ment to be played.

I played it back in the days with keyboard and still do :) Works for me.
It was never meant for a joystick, but for a gamepad, it was designed for the Playstation.

To play these old games on a PC with a controller, the best option is to grab a gamepad with thumbstick moving on a square (like flightsticks) - not the modern ones that have round thumbstick movement, that willl cause problems with some games. I don't know if Tomb Raider supports modern PC gamepads, but two of the games that cause problems are the original Lego Star Wars and Ultimate Spider-man.

It's always played absolutely fine for me with a keyboard. Tbh, I prefer using a keyboard to a joypad ...

Yes i can see only DosBox too (only for GOGGalaxy maybe doe to easiest one-click compatibility?). Although here it is - near pinned topic
http://www.gog.com/forum/tomb_raider_series/tomb_raider_update
where two fan-made fixes mentioned that is suppsoed to be native Windows solutions (unofficial native).

Try pinnacle game profiler :)