Okay so I recently had to do a gasket job, timing chain, and valve job on a 2011 Lr4 because it jumped timing due to the chain guide issue. I finished the job and went to try and start the engine and to my luck nothing just a single click. My first thing I did was check the engine to make sure it turned freely and it did. Then I swapped the relay for another one I know was working to make sure that was not the issue. Then I checked the battery and it was good but I replaced it anyway since I planned on doing that anyway. I then purchased a new starter and installed. Went to start the engine again and same symptom. I am at a loss now in trying to figure this out. Does anybody know what this can be?

 

My guess would be you left a ground cable loose doing the timing chains. If you hear a "click" from the starter (and its not something like the throttle body resetting), then the KVM, pushbutton, CJB and all that is working (it is saying its "OK" to crank). Then the fault is either power or ground to the starter.
My first guess is that you left the TDC pin on the flywheel, but if it turns freely, then its not that.

 

Check the Fusible link on the positive battery cable.

Also you can jump the contacts directly at the relay socket to confirm that it's not a relay issue.