That lever is for silent or strike. You have to make sure you have the wheels in the correct position both chime and strike in order for the chimes and strike to work. Also the cam wheel on the chime the gathering pallet on the strike. If you need help with this movement I can help you through it, just ask.
@HSL demonstrated how he disassemble, clean and lubes reversers. I am looking for his post, hopeful to find it and will inform you.
Considering your watch is a Tudor, I personally prefer and recommend new replacement.
If your mobile phone is in a flip case with a magnetic catch then all you have to do is leave your watch sitting on top of you phone for 5 minutes and bingo.... it can be as simple as that unless the watch has magnetic shielding.
Either way magnetism or sticky residue on the H/S are you most likely causes.