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My question is whether it is possible to graft or bud oranges onto my lemon
tree.

It is my understanding that all the citrus trees you buy are actually
lemon, orange, lime, etc grafted onto some other citrus stock.

At one stage it was common lemon stock as that had the best root growth.

You can check this out by looking at availabe stock on sale and see how
it has bumps in the stem/trunk.