The classic Meforshim do not explain where the wealth came from - and none of them claim it came from the Egyptians.
The all say that Lot became wealthy in Avraham's merit. E.g. Rashi:
ההלך את אברם. מִי גָרַם שֶׁהָיָה לוֹ זֹאת? הֲלִיכָתוֹ עִם אַבְרָם:
WHO WENT WITH ABRAM — What brought it about that he possessed all this? The fact that he was accompanying Abram (Genesis Rabbah 41:3; Pesikta Rabbati, שמיני).
This [and other sources] make it sound like it was a Gcd -given reward for hanging around a Tzadik.
Their source is probably Bava Kama 93a that says:
א"ל רבא לרבה בר מרי מנא הא מילתא דאמרי אינשי בתר מרי ניכסי ציבי משך א"ל דכתיב (בראשית יג, ה) וגם ללוט ההולך את אברם היה צאן ובקר ואהלים
Rava said to Rabba bar Mari: From where is this matter derived whereby people say: Drag wood after a property owner. In other words, help out a wealthy man even in a small way, as this may lead to your benefiting from him. Rabba bar Mari said to him that the source is as it is written: “And Lot also, who went with Abram, had flocks, and herds, and tents” (Genesis 13:5).
This makes it sounds like it's a natural cause; hand around the rich and you'll probably get rich.