Definitely not Battenburg which is a tape lace. I would have to see the motifs in person, but the sparse filling stitches with the infrequent picots imply that it is handmade. Those are definitely needle lace, but the flowers and leave are eithe machine made or if handmade, they are bobbin lace. Check and see if the filled in areas are evenly woven or irregular. Even would be machine made and irregular is probably bobbin. (there is also a difference at the edges but I can't explain it well in writing). The net it is attached to is also old-- possibly cotton-- nylon net isn't shaped like that.
A lovely piece if lave! Thank you for sharing!