What happens if Korthus and Leblanc die by Falling Star? Does Karthus effect count?

Yes, Karthus, Eternal's effect counts, and it will apply to any Deathknell effects that trigger from LeBlanc or any other units dying simultaneously with him.

According to RiftJudge FAQ #9028, FAQ #8974, and FAQ #9317, Karthus, Eternal's ability ("Your [Deathknell] effects trigger an additional time") is a passive ability, not a triggered ability.

Here is how the interaction works when Falling Star kills both units simultaneously:

1. Resolution: Falling Star resolves, dealing 3 damage to Karthus and 3 damage to LeBlanc, killing both units simultaneously.
2. Passive Persistence: Because Karthus's ability is a passive ability, it remains active at the exact moment the other unit's (e.g., LeBlanc's or another unit's) Deathknell trigger is created, even though Karthus himself is being killed at the same time.
3. Result: Any Deathknell effect triggered by the simultaneous death of another unit will trigger its base amount plus one additional time due to Karthus's passive effect.

Note: You mentioned LeBlanc in your question. Please verify the specific card version of LeBlanc you are referring to, as the LeBlanc I retrieved ("LeBlanc, Everywhere at Once") does not have a Deathknell ability. If your version of LeBlanc has a Deathknell effect, it will trigger twice; if it does not, there is simply no Deathknell effect for Karthus's passive to modify.