You are correct, there is no universal standard on the order:
In mathematical functions which do an universal conversion, between x,y or lon,lat or inverse, the lon,lat order should be used, because the x-axis relates to longitude and y to latitude and the x,y order is usually preferred.
Further, if you program a piece of code which is related to draw a lon,lat coordinate on x,y coordinates (screen), I also would use the lon,lat order because of the direct relation to x,y.
The order lat,lon is the classical one, coming from (old) navigation and geography. I assume that latitude in that field is used first because it was easier to measure (using only a ruler, the sun and a stick for length of shadow measuring).
The longitude was not determinable for long time. If you read old adventure reports, they only tell the latitude that their expeditions reached).
I think therefore they use latitude first, the measurement of longitude came later in history, once precise chronometers have been available and transportable.
So for apps that display coordinates info on a screen you should display latitude first.
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