To fully test this system, specialized LR specific diagnostic equipment is needed(many off brand ones, not just the dealer stuff)
But even if you go to the dealer for the diagnosis, ask them for a print out of three things for this fault.
1. A complete print out of faults, both related and unrelated.
2. A print out from the results of the DMTL(Fuel Leak Check) test.
3. A print out of your adaptive fuel trims(long term and sub-feedback)
The dealer equipment can do all three, and takes about an additional 2 minutes to pull it all(which should be done as part of the diag process they're already doing) but some of the off brand equipment(even the good ones like AutoLogic) does not have access to the adaptive fuel trims.
Even the dealers have incorrect diags pretty often for these faults, but with those three print outs, you can either pinpoint the failure, or at the very least, rule out some of the common issues.