methanol is pretty hard to wind up getting. There's very little produced when making alcohol and to be any danger, methanol has to be concentrated (distilled). Even then, there's usually pretty little, you have to save enough of it up to be a problem. The real danger of methanol is when unscruplous people added methanol to alcohol to "extend" alcohol and make more money selling it.
You are correct that wild yeast had gotten in and caused this to ferment a bit, and the closed bottle allowed pressure to build up and carbonate the beverage.
Chances are that it is safe. Wine, cider, and similar fermented items including bread originate by the getting wild yeasts from the air. Usually and ideally, what will happen is that the yeast (and certain good bacteria) take hold and don't allow the bad ones to propgate. A common cause of bad bacteria tends to be when people aren't hygenic. (If your mom didn't wash her hands, or the bottle, and was petting the family dog while using her hands to make this stuff, that's a bad sign. Also, if people are drinking from the bottle and then you let it sit around, that's also bad. Since you did say that this was the first time you opened, then you can exclude the bacteria that would propogate if you drank from the bottle.) most bad bacterias will simply taste bad.
(cider used to be just apples, crushed/pressed into a clean container and left sitting out to start fermenting and could be sealed to carbonate.)
The acid from the lemonade also prevents many bacteria/spores from growing, or slows the growth which is probably why the bottle didn't explode some time ago.
I'm not going to go so far as to say it's safe, since I don't know what processes were used, but I think there's a good chance that it is. Again, the key part will be sanitation to avoid bad bacteria.
Secondary: GF Czech Lager
Waiting to be kegged, Italian Primitivo
Kegged&Ready: GF Orange&Coriander, GF Honey Lager, GF chocolate ale, GF English ale, Island mist (zinfandel), Island mist (cbry malbec).
Bottled: Infected Mead, Dry Hard ciders, Accidental Sorghumwine, various unnamed.