I have an LR3 2006 model.
I noticed when I am stationary the rpm dives from idle to almost cut out and then back again, this also happens at low speed the engine has cut out a few times.
I think it does it when the outside temperature is hot, I live in Oman and at the moment can get into the 40's
Any ideas?

 

Could be a dirty IACV and/or throttle body.

 

X2 on throttle body.

remove intake hose and use something semi toxic on a rag to clean inside the throttle body by pushing butterfly open and wiping.