Potentially. Like the other poster said, you can go through Github, but if worst comes to worst you could take screenshots of what Lovable makes and have Cursor modify the UI based on the screenshots. If you're using Sonnet 4.5 as a model it should be able to handle it pretty easily.

You can have Lovable do the design and then sync it to a GitHub repo. Then you can pull it down locally and further refine with Cursor.

Just be aware that under the hood Lovable is strictly react (or at least it was the last time I checked it) so that might be a important variable to consider since I saw that you were using Laravel.