Here;

https://www.lexussouthatlantaparts.com/showAssembly.aspx?ukey_assembly=773895&ukey_make=1082&ukey_model=15669&modelYear=2000&ukey_category=21750

 

That's your PCV hose so more than likely your PCV needs to be changed. The missing hose connects to the other sideof the black box in the pic but it looks like the fitting has snapped off which is a common problem.
​​​​​​https://www.clublexus.com/forums/ls-...r-cleaner.html

 

VERY IMPORTANT! The insulated vacuum hose from the PCV valve on the driver's side commonly has a crack in the back of it where it connects to the intake. This will make for bad idle and intermittent no starts. DO NOT cap off the PCV valve and intake fitting and start the car. You will build up lots of pressure in the engine and pop your valve gaskets in under 5 minutes. The other photo on the passenger side is a vacuum that connects to the black box integrated into the air filter/ducts. It must be connect to the fitting on the box. Do not leave any vacuum fittings open or run the risk of only being able to start an LS400 when it is 70-75 degrees outside. OEM hoses are best but expensive. I used 1/2" fuel line for $1.50 a foot and new clamps. GL

 

The fitting is broken off on your black box. Left of the bolt in the middle of the picture. I believe there are 3 fittings that break easily on the black box. Be very careful taking the black box off. The fitting are plastic and will snap off if the hose is still attached. Best way I have found to replace the fitting is tapered pipe fittings from the hardware store. Either heating a copper pipe fitting and melting it into the hole or plastic pipe fittings and gasket seal/wait 24 hrs to dry. Also, be mindful of all the bolts on the box and the air ducts, they can break easily too. Don't over tighten anything, or you might even be drilling and tapping an aluminum block.

 

 

 

Didn't you see this?
https://www.clublexus.com/forums/ls-...ml#post8495863