Ls400 engine vibration

[LSfamily]

I've just acquired a 2000 LS400 and as I'm driving down the highway, I noticed a vibration that seems to have started immediately. I put it in neutral at 70mph, it goes away. Put it in park and rev, vibration builds slightly. It's not terribly noticeable but anybody familiar with these cars would notice immediately. Please help I am suspecting misfire? Also I have no clue when or if timing belt has been done. Odometer reads 150k however I noticed some 250k readings earlier this year on vehicle history report. Also no codes. 

[LSfamily]

Also vibration is present at idle. I love these cars and have my wife driving a LS430 and want to keep these cars in the family for 10+ years but only if they are in perfect condition!

[steve2006]

You really need to establish if there is a misfire although this normally generates a fault code and illuminates the Engine Management Light or if it is due to a mechanical fault like the engine mountings or transmission mount.

When was the last time the spark plugs were replaced?