No, that’s not true.
But, what is true is that lemons are much more vigorous than limes or oranges, and if you don’t aggressively prune them (which you won’t, believe me), you eventually end up with just a lemon tree.
Essentially all citrus trees in commercial production are grafted. And no, the effect of the rootstock (or the other scions) on a scion doesn’t change the flavor over time.
But it’s quite common for multi-grafted trees to eventually end up being all the most vigorous scion. I don’t live in citrus-growing territory, but it’s a known issue with multi-grafted apple trees and stone fruit (plum, peach, etc.) trees, and I’m sure citrus works the same.
At one point, I was growing 20+ varieties of citrus. I used to make a delicious Blood Orange/Tangerine/Navel Orange juice mix. I also used to pack up boxes of my Lemons and send them to my sister in NJ, so they could make Limoncello. Sadly (for me), we chopped them all down to put on an addition to the house.
I used to have a potted Myers lemon. I kept it indoors in the winter, and planted it each summer. The lemon flower certainly smells wonderful. But it’s not an especially pretty tree, and i like to eat the fruit.
I miss our lemon tree, and am coming to the position that if the multi fruit tree becomes lemon only, it would be fine, and I’ll likely have sold and moved on.