The good news is, marking a project as 'Lost' will ensure the deposit and any payments already made are still captured, and you can still report on that income.
Marking a project as 'Lost' will automatically move the projects into your Archived Project section (Article), so you can still report on revenue, even if the project is lost.
'Lost' projects cannot be signed by the client (Article), but you can always duplicate the project (Article) to make a 'New Project' copy.
If you have the QuickBooks Online integration active, it will Void the invoice in QuickBooks (Article).