As for infinity being a “lazy eight”, the Wikipedia discussion of the infinity symbol notes that: ”...before typesetting machines were invented, ∞ was easily made in printing by typesetting the numeral 8 on its side. ” The article agrees with @Vortico in explaining that the figure ”...is sometimes called the lemniscate, from the Latin lemniscus , meaning ‘ribbon’. John Wallis is credited with introducing the symbol in 1655…” Wallis might have borrowed symbols for large numbers from ancient alphabets.
According to this blog the symbol is “New Latin lemniscata , from feminine of Latin lemniscatus with hanging ribbons, from lemniscus ” [Attribution given to Meriam-Webster online but I can’t find it.]
In any case there’s no mention of Möbius bands (sorry, @the100thmonkey) & no apparent connection to 8, eight-letter words—or any kind of “8-ness.”
This confirms my initial hunch that it’s just a coincidence. Such occurrences are more common and likely than intuition would suggest. Like all of us humans, @Ltryptophan‘s brain is searching for pattern & meaning in the pageant of life. Didn’t pan out this time!