Your Supabase URL and key aren't in the repo because they live in Lovable's environment, not in git (which is correct).
Create .env (or .env.local) next to package.json:
VITE_SUPABASE_URL=https://yourref.supabase.co
VITE_SUPABASE_PUBLISHABLE_KEY=eyJ...
Open src/integrations/supabase/client.ts to see the exact variable names your project reads, older Lovable projects use VITE_SUPABASE_ANON_KEY. Values are in Supabase → Project Settings → API. Restart npm run dev after, Vite only reads env files on startup.
And add .env to .gitignore before your next commit.