Yes You can open LiveSplit, right click and choose the one that says "Settings". The first chart says "Hotkeys" Here you can Click all the options for example: Start / Split. You can select the key that you want. I use the NumPad 1. If your problem is how to stop the timer, there's an option called "Pause". Choose the key of your keyboard that you want and problem solved. Any other problems?
If using an emulator or the steam release, just use the autosplitter, and make sure you right click - compare against - game time.
If using console, or you don't want to use the autosplitter, make sure you are also comparing against game time like above, but right click - Edit Layout- Click the add button - Control - Manual Game Time. When you start the timer, a dialog will pop up for you to enter in the IGT.
Results of Community Vote:
For RTA-TB: 24 (96%)
For IGT: 1 (4%)
The result is not close and is why this vote needed to happen.
The default timing method for Sonic 1 1991 moving forward is RTA-TB. IGT is still relevant as a secondary timing method.
-Sonic 1 Mod Team