1.37 is ISO/BS so this is a left-handed thread. It's neither lefty-loosey or righty-tighty, rather it's lefty-tighty and righty-loosey. You are correct: clockwise to remove. I have access to a tool similar to a VAR 30 for ornery fixed cups and it works beautifully. Another option that has worked well is to clamp the cup in a bench vise and then use the frame as leverage while turning.
Also, if you don't plan to replace the bottom bracket you can leave the cup in place.
Good luck,