Lilac Pink is a lovely soft warm neutral with a whisper of dusky pink-lilac to it — the kind of colour that reads almost as a putty in north light and warms up beautifully in the sun. Edward Bulmer's natural paints are gorgeous but they carry a premium price, so I understand wanting a like-for-like at less cost.
Good news: the matches here are genuinely tight.
Crown Sandstone is your closest, sitting at ΔE 1 from the original with an LRV of 60.6. A ΔE under 1 is essentially imperceptible to the eye — you'd not tell them apart on a wall. Crown is widely stocked, trade-friendly and a fraction of the Edward Bulmer price.
Dulux Labrador Sands 4 is right behind it at ΔE 1.1, LRV 59.4. Also brilliant, also cheap, and Dulux availability is everywhere. If you can't get Crown mixed locally, this is the one to grab.
COAT Weekender comes in at ΔE 2.7, LRV 60.8 — still a very respectable match, just a touch further off than the other two. COAT's worth a look if you want a lower-VOC water-based paint with a nicer finish than standard trade emulsion.
The "but what about" here: the thing you lose going from Edward Bulmer to a mainstream brand isn't the colour — it's the natural pigment formulation. Bulmer's paints shift subtly through the day because of how natural earth pigments behave in changing light, and a synthetic-pigment match won't do exactly that. For most rooms you'll never notice. If the colour's going somewhere with dramatic light swings and you specifically chose Bulmer for that quality, stick with the original.
For everyone else: get Crown Sandstone or Labrador Sands 4 mixed up, buy a tester, and paint a decent patch on two walls before committing. At ΔE 1 you'll be sorted and several quid better off.