When putting on a shoe with buckles, should I close the left buckle first, or is that only with laces?
There is a debate among poskim concerning this matter, the question being whether the issue is limited to tying laces, which is similar to tying tefillin, or whether the idea applies to any form of fastening.
After mentioning the different positions, Rav Menashe Klein (Mishnah Halachos Vol. 13, no. 3) writes that one should fasten the left should first even where it is not being “tied” with laces.
Because we are fairly used to this practice, and it does not involve any expenditure of effort, it seems right to follow the advice — even for the reason of maintaining the “habit” of fastening the left should before the right.