rattle in 04 grand marquis engine

Have someone check out your cam phasers and cam chain.

Have you had any work done recently?

Had intake manifold replaced four months ago

Are you sure this is an engine rattle or could it be an exhaust system heat shield rattle?

It sounds like under-pressurized lifters. Doesn't rattle at higher speeds

The oil pressure needs to be checked with a mechanical gauge.

Could this rattle be a catalytic converter?

It is possible. Take a rubber mallet and strike the converters to see if they rattle.