Will executing a Bitcoin transaction (with Electrum) at the exact moment when the green transaction graph of
https://mempool.space/ reaches its lowest point result in lower fee?
No, not exactly but you are close. Because the green graph on mempool.space is used to show the number of transactions that are not confirmed yet (pending transactions). So if it is lower then it ofcourse reduces the competition level for such block space therefore the fee tends to be lower, however, the time taken to confirm this transaction is not guaranteed.