In Legend of Tomorrow S01E16, Sara goes to the Arrowcave and meets her dad and got the information about the death of her sister and after some chit-chat she leaves.
But chronologically when does this specific scene occur corresponding to Arrow?
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It all happened during the Arrow episode viz. S04E22 (which aired the previous night on television).
The event went like this:
Felicity was at the Arrowcave and then Quentin Lance came there. They were tracing Thea's location; they got it and Oliver and Diggle went to search for the place. Meanwhile, Felicity received a phone call from Curtis and left the place. Then Lance said:
Alright, I'll cover comms. If I hear anything I'll patch you in.
Then he sat down at the console. Sara arrived shortly after that moment to find him alone in the bunker and sitting in the same place.
Notice the shirt that Quentin Lance wore in the two concerned episodes: