Need window handle
I believe you have an older style casement lock with a rectangular body. Take a look at our 38-138 lock with a 29MM long fork. You will need to remove your lock from the window to compare the fork length and confirm that these match. Also take a look at the 38-139, which has a longer fork. That's another option.
Your lock being broken will be a problem. Try pushing the lever handle back into the lock body to unlock the window. Hopefully this will activate the locking mechanism and allow your to unlock the window to access the mounting screws to remove the broken lock. If not, your options are limited. You'd have to find some way to cut the lock off the window, which is not easy. We highly recommend contacting a local professional in that circumstance.