Slaked Lime sits at the pale end of Little Greene's card — a cool off-white with an LRV of 87.5, which means it's doing the job of a white in your scheme, not a mid-tone. Treat it that way and the pairings fall into place: it's the light, and everything else you choose sits below it.
The natural first partner is Paint & Paper Library Slate IV (LRV 67.5), a warm grey-green with an olive, khaki lean. It's noticeably deeper than Slaked Lime, so run the pairing that way round — Slate IV on walls or panelling, Slaked Lime above on ceilings, cornicing and woodwork. That cool-over-warm layering is what stops an off-white scheme feeling thin.
To take things deeper, Mylands Artichoke BH.13 (LRV 27.6) brings a muted, earthy olive that's lovely on joinery, a cupboard run or a chimney breast. And for a proper anchor, Dulux Sapphire Springs 1 (LRV 6.4) is the drama note — a deep slate-blue for a feature door or panelling that makes the off-white read even crisper.
The 'but what about metals?' question: Slaked Lime's cool cast takes nickel, chrome and pewter easily, but because Slate IV and Artichoke pull the scheme warm and green, aged brass works too — pick one lane and stick to it rather than mixing.
Practically: paint two coats on A3 boards you can move about, and look at them morning and evening — in the darkest corner of the room as well as by the window. Slaked Lime will read almost pure white next to Slate IV and more definitely off-white against a brilliant white, so decide what it's sitting next to before you judge it.