Well that fall/ spring stuff is more about deciduous trees in cold winter climates. I think for lemon trees which are ever-bearing, in climates without much frost (I'm not sure where colton is, but you wouldn't be growing lemons in a wintry climate), I think winter is the best time to transplant it. The idea of the fall spring stuff is you transplant deciduous trees when they are dormant. Winter is the slowest growing time for the lemon tree, so that's when to transplant it.
Remove any fruit on the tree, so it can focus on growing more roots. Dig the hole where it is going first, so you don't let the tree roots sit in air for any longer than to move them from one hole to the next and preferably wrap them in burlap or something while you do that. Dig the tree out with a root ball as wide as the dripline of the tree. Plant it so that it is at the same level it was. Water in well and you can put some rooting hormone in the first watering. After that mulch well, keep well watered, but NOT soggy.