Bonjour Ly ! "Lorsque" actually means the same as "quand" (when), so it's a bit different from "while". It doesn't mark simultaneity so much as something happening at one specific moment. The best way to express simultaneity in this sentence would be as such: "Je fais la vaisselle pendant que tu arrives." (I do the dishes while you're arriving.) However, the use of "arriver" here feels a bit weird, as it is not an action that lasts as long as doing the dishes, so the simultaneity here feels a bit contrived. Something like ""Je fais la vaisselle pendant que tu fais le lit." (I do the dishes while you're making the bed.) feels a bit more natural. I hope that's helpful!

Yes, "pendant que" would be "while". "Pendant" on its own means "during".