If you want Travertine in Dulux, go for Bracken Salts 4. At a measured ΔE of 0.8 from the original it's an imperceptible difference — once it's on the wall you'd struggle to tell the two apart, even side by side. It also lands at LRV 61.8, so you get that same soft, light-but-grounded warmth that makes Travertine such a useful neutral.
The runner-up is Dulux Trench Coat at ΔE 1.2, LRV 62. That's still very close — under 2.5 is the threshold where most people can't spot a difference in normal light — and the slightly higher LRV means it'll read a touch lighter. If you can only get one, Bracken Salts 4 is the better call.
Now the honest bit, because this comes up every time: a colour match gets you the hue, but it won't give you Little Greene's finish. Travertine in Little Greene's Intelligent Matt or Absolute Matt has a depth and a chalky, light-absorbing quality that comes from the pigment load and the way the paint is made. Dulux Heritage Velvet Matt is the nearest Dulux equivalent for that kind of soft, flat feel — if finish matters to you, spec that over standard Dulux Matt.
Where you'll really notice the match holding up is in north-facing rooms. Travertine and both Dulux matches sit in warm-neutral territory, so they keep their warmth in cooler light rather than going grey on you — which is exactly why people reach for this colour in the first place.
Practical advice: don't trust a fan deck or a screen for a match this tight. Order a Dulux Bracken Salts 4 sample pot, paint two coats on a bit of lining paper, and tape it up next to your existing Travertine or against the trim you're keeping. Look at it morning and evening. At ΔE 0.8 it'll be sorted — but seeing it in your own light is the only way to be properly sure.