First off, all hail boognish. Ween rules.

That said I think it’s related to cooking. I used Google Ngram to search for it and found a "lost in the sauce" reference in an 1896 cookbook.

https://www.google.com/books/edition/Cassell_s_new_universal_cookery_book/mf7fq2HT8YwC?hl=en&gbpv=1&dq=%22lost+in+the+sauce%22&pg=PA105&printsec=frontcover

Not the colloquial usage, but the earliest usage I could find.

He may not have coined the term, but Gucci’s full quote is an all-timer

If a man does not have sauce, then he is lost. But the same man can get lost in the sauce.

While I don’t think he’s a good rapper in the technical sense, there’s something I absolutely love about Gucci. I play his East Atlanta Santa Christmas songs this time of the year, every year.

that pig's a pretty mean bastard

https://pmc.ncbi.nlm.nih.gov/articles/PMC2724753/ Lost in the Sauce The Effects of Alcohol on Mind Wandering? 2009 Aug 11

An article on the National Institutes of Health's site predates Mr. Mane by four years.

Paint the town brown 🤘

Urban dictionary, 2006

https://www.urbandictionary.com/define.php?term=lost+in+the+sauce&page=2

Lost In The Sauce Listen to pronunciation Share definition When you begin to have intercourse with every intention of using a condom, however you start off without one. At some point you say to yourself im going to get the condom, but you never do. In her moisture, the sensation is so good, you never bother to get up and get one, therefore remaining raw. Short term; going raw, no protection. "Man this girl was so fine that we started off with the foreplay and before you know it, I was Lost In The Sauce." by Jay Denson August 17, 2006

"Lost in the sauce" is an old phrase, at least as long as I've been alive, where "sauce" is alcohol.

All I know is the first time I heard it was back in 2007 when I was in USMC boot camp, and one of the drill instructors said to one of the struggling recruits, “You’re just a poor little SpaghettiO, lost in the sauce” and I had to hold back that special kind of maniacal laughter that comes from being sleep deprived to avoid shifting that drill instructor’s focus in my direction.

I’ve loved that saying ever since

That song was part of my ukulele busking set back in the day, and I still play it for myself now and then. Weirdly, that's the only Ween album I've ever really gotten into. l also play Cold Blows The Wind and The Blarney Stone from that album. It's such a good album.

I always thought it referred to being drunk. Sauce being a euphemism for alcohol.

This seems pretty obviously from cooking. If you don't put enough of an ingredient in, it gets lost in the sauce, meaning you can't even detect its presence.