In Lovable: GitHub → Connect to push the project to GitHub. Private repo? Use https://<token>@github.com/you/app.git
https://<token>@github.com/you/app.git
On the old host install the Site Mover plugin → Tools → Site Mover → Create export → Download. Upload that file here.
If a WordPress site with this name exists, it will be overwritten.
Empty repository = use the last uploaded ZIP.