Are talking about the top player or the bottom?

The top player is the one grabbing the lapel around and applying a cross face, I'm asking what can be done as the bottom player to fight that grip.

Just to clarifiy is this where the pull the lapel out of your belt, and pass it over your elbow?

If so:

So once that lapel is across that is a problem, you need to do big movments to get out and it can be very tight. When you notice that lapel being manipulated you can guess what is coming. I like to take my arm and put the forarm into the top players armpit to hide it. The aim being to prevent the lapel from going between my elbow and my wrist. You can off blance the top player by pushing the armpit over your hips.

Let me know if I am miss understanding. Possibly post a photo?

My bad, I should have included a picture from the start 😅

From the position in the image a solid hip bump with a frame against the neck and stomach to carry the top player over your head should allow you to bring a knee back in. This knee should allow you distance your head from the top player and recover a guard.

Thanks I'll give it a try next session. What if he sits out while holding on to the same grip ?

From there push the top player towards your legs and throw the far side leg Infront of his face, collect his arm that's behind you and armbar him.

Oh nice, thank you very much !

Welcome bjj is hard to explain in text form so I hope I am helping

Definitely, I was able to picture the movements you described well, now whether I will be able to pull it off as easily is another matter !

Do NoGi!

FACT.

I started in nogi and didn't have any difficulties escaping from all positions, so I decided to switch to gi because apparently grips and friction force you to have proper technique in order to escape successfully.
I plan on going back to nogi when I start working on my attacks.

Avoid the shoulder pressure then hip escape to Half Guard or Full Guard.

A lot more options.

Enjoy the journey