I was wondering if that was common, and what tips and tricks you have for using lipstick on eyelids. What about creasing? And could it irritate the eye area?

No... I would not.

Just because a pigment is FDA cosmetic, that doesn't mean it's safe for use on the eyes. Cosmetic Pigments are approved based on body part - any, eyes, lips, etc. Many reds are approved for lips, but not eyes.

Thanks for the info! I was asking because I once saw a pro MUA doing this on a TV set. Though it was fine but I did have some doubts.

That is true… It is a different formula meant for the lips. I would be more worried about red pigments. However, If I get confirmation from the brand/representative that a certain lipstick is safe around the eye area, I don't have a problem using it, if it is all that you have in your kit.
I actually prefer grease paints, I've used them all over my face, I even used a red grease paint on my waterline (knowing that it was safe to do so). If you want the same texture as a lipstick, grease paints could be the closest thing, or cream paints.

If you did use lipsticks around the eye area, it would be more for an avant garde look. Getting it to not crease, would be nearly impossible because lip sticks are very emollient.

I've used eyeliners on the lips, lip liners on the eyes. As long as you get confirmation that it is safe to do so, it should be fine. Brands should have this information about each product/color.