We actually have a video on how you can fix this issue. I recommend watching it, this should be of help to you.
Once the lock is removed, we need a clear picture of it out of the window and without obstruction so that we can recommend a match.
In that case this could be somewhat of a big project. You could try to slip a putty knife between the frame and sash to manually throw the lock, but this isn't possible on all windows. If that fails then your only remaining option is to cut the lock off the frame, which is a hassle (to say the least). In that scenario I absolutely recommend contacting a local professional to come out and handle it for you. That's not an easy project at all.
Thanks for removing the lock, I know that had to be some trouble. Unfortunately the lock you're showing me is lacking the arm, which is the most important detail. For now I think your lock is similar to our 38-091 and 38-092, but without seeing that arm I cannot confirm. You could also have our 38-099 or 38-100, or others. Start with these at least and see what you think.
That's not the arm I mean. I'm talking about the locking arm, the piece of the assembly that physically goes into the frame and interacts with the tie bar. If you look at the products that I linked you two in my last response you'll see what I mean.
