If Ruined Rex dies in a combat showdown and deals 4 damage to a unit on another battlefield as that showdown resolves, does that damage heal?

No, the 4 damage from Ruined Rex's Deathknell does not immediately heal.

Here's why: the Combat Cleanup's "Heal all Units" step (Rule 461.1.a.1) happens before the pending Deathknell trigger resolves — not after. As established in RiftJudge FAQs #10018, #10182, and #10410, the sequence is:

1. Combat Damage Step — damage is dealt, Ruined Rex dies and its Deathknell becomes pending on the chain.
2. Units with lethal damage are moved to trash.
3. Heal all Units — everything on the board has its damage cleared.
4. Deathknell resolves — dealing 4 damage to your chosen enemy unit.

Since step 4 happens after step 3, the 4 damage lands on a freshly healed board. There's no second healing wave unless another Combat Cleanup starts at that unit's battlefield, or the turn ends. So that 4 damage stays marked on the target until the end of the turn (Rule 143.3.b).