Also on the day before whitney hike, we are planning to do some acclimatizing hikes in Lone Pine area.
Where in the Lone Pine area? Most of Lone Pine is well below 4000 feet, so you aren't going to get any positive effect there.
One good place is right at Whitney Portal on the day before your hike. You briskly hike up to the first stream crossing and check it out in broad daylight. That gives you half a chance of getting across it during the middle of the night and still have dry boots.
After years of refining my technique, I found the best place for acclimatizing is in the White Mountains. I would hike up and down White Mountain Peak. Then from my time on that, I could project how I would be doing a few days later on Whitney.