when engine is running there is rattling coming from under car
First thing I tell people is to look for a loose catalytic converter heat shield.
Could it be loose or worn out motor mounts? Worth looking at.
As Tom said, 99% probable it is the heat shield.
Looking for a Used GS 300 in your area?
CarGurus has 733 nationwide GS 300 listings starting at $1,499.
Search Lexus GS 300 Questions
Lexus GS 300 Experts