These are not oxymorons. A lot also depends upon which definitions you choose.
"Brier (briar)- A prickly thorny bush or shrub in general; formerly including the bramble, but now usually confined to wild rose bushes." Oxford English Dictionary. Not sure when the bramble disappeared in usage from the general understanding of the concept 'brier.' I presume the original understanding of the line in that version of "Lord Lovel" was the rose twining with the bramble.

Poets have referred to love being a killing thing for some time. And who doesn't know the Oscar Wilde poem with the line, "Yet each man kills the thing he loves, from all let this be heard." This may be considered a 'paradox,' but oxymoron? No.

The term brier has also been applied to the white heath (pipes may be made from its roots), but that doesn't apply to the ballad.