Lat Long or Long Lat

There seems to be no standard whether Longitude,Latitude or Latitude,Longitude should be used. WSG84 and stuff based directly on it, seem to prefer Long,Lat.

"Normal people" always tend to speak of Lat, Long - so I've very often seen code or frameworks that use Lat, Long (e.g. google Maps)

Is there any strong argument for either way?

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.

As mentioned in the comments by @Midavalo, there is a standard for the representation of geographic locations by coordinates: ISO 6709.

It describes that a geographical point is specified by the following four items:

• a first horizontal coordinate (y), such as latitude
• a second horizontal coordinate (x), such as longitude
• optionally, a vertical coordinate, i.e. height or depth
• optionally, an identification of the coordinate reference system (CRS)

The order, positive direction, and units of coordinates are supposed to be defined by that CRS, but when such a CRS identification is missing -- which is very often -- the data must be interpreted by the following conventions:

• Latitude comes before longitude
• North latitude is positive
• East longitude is positive
• Fraction of degrees is preferred over sexagesimal (degrees, minutes, seconds) notation

So, unless another coordinate reference system is mentioned, the standard is "latitude, longitude, (elevation)".