Fwiw I think in the fuzzy world of square tapered bb with various historic "standards" nothing is certain until tried and tested, and it probably depends on which 124mm bb.
If it is 3NN in
Sheldon's database, then the 122.5mm/NL Shimano UN54 bb is likely to be ok although I believe the left side may be around 3mm short (because not only the NL is shorter it is also asymmetric). If only the spindle requires replacement, then a more reliable alternative may be to buy something like
this.
If it is the 3U then the UN54 127.5mm/EL, which is 3mm longer on the right than the NL, will deliver a better chainline, or alternatively
this.
There are other possibilities, so a clearer identification of existing might help.