Is it necessary for the lead to execute all four directions or can the lead choose to simply go just forward and back/to go just side to side?
Not at all. In fact, in our syllabus, they are listed as separate figures (or rather, they are listed as two variations of the same figure). We call them Hesitations, but the figure is the same.
Not only can you dance the forward-back Hesitations separately from the side-to-side Hesitations, but you can also dance a single Hesitation in any direction without the need to follow it with a Hesitation in the opposite direction. One particularly popular combination is a LF Forward Hesitation followed by the 4-6 Left Box Turn (i.e. the second half of the basic Box Step).
For more complete information about Hesitations, I suggest you read the Overview tab on our Waltz Hesitation page:
https://www.ballroomdancers.com/Dances/info.asp?sid=110This page gives a very thorough explanation of Hesitations, including suggestions of different ways to combine them with other figures. And for a really thorough list of ways to combine them, click on either the "preceded by" or "followed by" tabs and try them all!
Regards,
Jonathan Atkinson