What happens if I discover after closing that a key piece of equipment was actually leased, not owned?

If the purchase agreement represented that the seller owned this equipment outright, or listed it among owned assets in the disclosure schedule, and it turns out the seller only leased it, that's generally a straightforward breach of a representation about ownership or title to the purchased assets, supporting an indemnity claim subject to the negotiated survival period, cap, and basket that apply.

This also creates a practical problem separate from the claim itself: if the business genuinely needs that equipment to keep operating, you may need to deal directly with the actual lessor to keep using it — assuming the existing lease, negotiating a new one, or replacing the equipment entirely — which is an operational issue distinct from pursuing the seller for the misrepresentation. A basic lien and asset search against the seller before closing, of the kind that's part of standard due diligence, is usually what catches this kind of gap before it becomes a post-closing dispute at all.