Livid is a properly grown-up grey-blue, and the trick with it is to lean into that coolness rather than fight it. The clean move is a chalky cool white on the trim and ceiling — Farrow & Ball::All White (LRV 92) is about as honest a white as you'll find, no yellow undertone to muddy things, so the contrast stays crisp and the room feels calm rather than clinical.
For hardware and metalwork, stick to slate and nickel. Yellow brass clashes with Livid's blue and makes the whole scheme look like it can't decide what it's doing. Polished or brushed nickel reads cleaner and lets the blue do the talking.
Where it gets interesting is the accent. A wall of cool blue can tip towards cold, so you want something warm and a little earthy to stop it — a soft oxblood or warm leather tone does the job. Paint & Paper Library::Blue Blood (LRV 16.4) is the deeper, dramatic route if you want a moody pairing on a chimney breast or joinery, while Dulux::Fuchsia Falls 2 (LRV 29.8) brings a warmer pink-toned punch for cushions, a feature door or a smaller adjoining space.
If you'd rather keep it light and breathable, Mylands::Beehive Place No.140 (LRV 58.6) sits as a gentle warm neutral that lifts a Livid-heavy room without throwing the cool palette off balance.
The "but what about warmth?" question is the one everyone asks — and the answer is texture, not yellow. Bring it in through timber, leather, and a wool rug rather than warming up the paint itself. Keep the painted surfaces cool and let the soft furnishings do the heavy lifting.
Practical tip: paint a big A2 board in Livid and stand it against your chosen white and accent in the actual room. North-facing light will deepen Livid considerably, so test it where it'll live before you commit the whole scheme.