The leaves look different to those on the main plant so I would assume that they are suckers from the dwarf stock that the lilac is grafted on. I would remove them but others may have other ideas.
After you remove them (cut close to the main stem, or bend horizontal and they may snap off cleanly if you are lucky) but they will probably keep coming back as Hazel 1 mentions, so rub off any new buds you see forming anywhere on the main trunk below the crown in the future.
A trowel in the hand is worth a thousand lost under a bush.
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it’ll help prevent it regrowing.
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.