You need some sort of medium to host the bacteria that're gonna grow during the cycle. A lot of people use
LR for that. The LS will do some of that, but depending on the size and type of tank you're setting up, you prolly won't want to rely on that. Also, the bacteria that generally lives under your sand is anaerobic, which means if you mess around with the sand and stir them out of it, they'll die and your cycle will be back to square one.
You need a source of
ammonia to cycle, so I don't know whats going on with just the LS... from your numbers it looks like you had a little cycle. Keep in mind that every time you add
LR you're going to have a mini cycle, so
imo its best to get as much of your
LR in the tank as you can at one time to avoid stressing out your livestock and then just waiting out the longer cycle.
I dunno why your
pH is jumping around like that... Whats your lighting cycle like? That effects the
pH.
Do yourself a favor and start testing your water every day or every other day, not just when you add stuff to the tank. You'll get a much clearer picture of your cycle and whats going on in your tank.
Also, you might wanna raise up the
salinity a bit. 1.021 is sort of low. All the
LFSs I go to keep their tanks at 1.025.