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?
I am having hard time understanding what you are saying here. Are you interested in creating and broadcasting a TX that pays less than 1sat/vbyte fee or are you looking for the TX to be included in the next block?
Even a TX with zero fee can be included in a block if the miners decided it to be, so high fee doesn't mean it's in the next block but the logical reason that mempool prioritizes the TXs that pay a higher fee so obviously if you are paying that is enough to be included in the next block for example at present you need around 0.33sat/vb.