If I have a Karthus and a Deathknell card die from a Falling Star, does the Deathknell still trigger twice?

Yes, if you have a Karthus on the board and another unit with a Deathknell effect dies at the same time (such as from a Falling Star), that unit's Deathknell effect will trigger twice.

According to RiftJudge FAQ #5353:

• Ruling: When Karthus and another unit die at the same time, the other unit's Deathknell triggers twice.
• Reasoning: Karthus's ability ("Your [Deathknell] effects trigger an additional time") is a passive ability, not a triggered ability. Because it is passive, it remains active and applies even when Karthus himself is being killed simultaneously with the other unit.

This is distinct from triggered abilities (like those of Viktor, Leader), which cannot trigger if the source leaves the board at the same time the trigger condition is met. Since Karthus is a passive effect, it successfully modifies the Deathknell trigger of the other unit as it occurs.