Um...okay.
The machine you're talking about is Mr. Fusion, which Doc had installed in 2015; seriously - it's not on the car until he comes back from the future at the very end of Part I. Ergo, it wouldn't have existed even back in 1955, and with plutonium not readily available in that time period they didn't have any choice but to rely on lightning.
Next, they USED Mr. Fusion. A third of the way into Part II, Doc throws more trash into it after they rescue Jennifer in 2015 and get ready to come back to 1985.
Finally, the only other time you see lightning is at the end of Part II, and then its effect is completely accidental. There's no lightning of any kind in Part III because it's no longer necessary by that point - the car still has Mr. Fusion (BTW, Mr. Fusion only powers the time circuits and the flux capacitor).