I'm not positive but I don't think she tangles with them...unless someone else has seen it? When they were after me when we were fighting the dragon, she didn't or couldn't fight the giants.
When I was in a similar situation, while I was fighting the dragon I saw Lydia attacking a giant. It was the giant that killed me after I got the dragon and when I went back to my last save, things happened differently. The giant had his mammoth herd and joined in with us in fighting the dragon and then just carried on his way and was non-hostile. I found out about the health potions thing on my own. I only gave her a couple and found out that one was gone when I checked back later. I didn't have much to spare though, as some of the tougher opponents can have me using up quite a few myself in the middle of combat.
For one of my other quests I took along the warrior woman from the tavern in Whiterun instead. In the ruins we encountered another woman, a mage it turns out, who joined us in our search. But the mage was a little careless/indiscriminate in where she threw down her fire attacks during fights and hurt the warrior woman. So the warrior started attacking the mage. But neither of them could kill each other. They would just reduce the other to kneeling for a while. Although I thought I was going to have to kill one of them to end the dispute, I used a healing spell on them instead and they returned to being non-hostile to each other after that. I haven't tried healing a follower when they turn hostile on you (from one accidental hit too many), but it may work the same if someone else in that situation didn't want to have to be forced to kill the follower.