I live in Patterson, La and I have some bare spots in my St. Augustine grass
under some pecan trees and white oaks that do not get too much direct
sunlight. I tested the PH level of the soil with a direct contact probe and
I'm averaging around 6 to 6.2 for a ph level. Ironically, I checked the
soil under a different area where the lawn is very dense with plenty of sun
and the results were around 5 to 5.5 for the Ph level.

Why is the Ph level where the grass is growing nicely so low where I
understand the ph level should be close to 7.0 ??

I plan to core aerate my lawn and lime afterwards to bring the reading
closer to 7.0 in the bare areas under the tree.

Do you think it's not too late in the summer to core aerate and lime. I
plan to use "dolomitic limestone".

Should I use pelletized or ground limestone ?

Your advice is much appreciated.
Ray