I find something very strange. Lot gets kidnapped; Avraham goes to war to get him back. Sarah his wife gets kidnapped; he does and says nothing. What is with this very strange discrepancy?
The Zohar says that Avraham was confident that his wife's merits would protect her (see here).
If so, it is readily understandable why Avraham had to go to war for Lot. Lot did not have the merit to protect himself.
The discrepancy between the three kidnapping cases in Bereishit- twice with Sarah (Pharaoh in 12:10–20 and later by Gerar's king 20:1–18) and once with Lot (14:12–18), is that Lot was taken as an act of war (spoils), so he responded with an act of war in return. Sarah, on the other hand, was taken by the two kings while Abraham was a guest in their respective countries. Abraham told the two kings that she was his sister, in a bid to save his life, since apparently the king of a locale had rights on the women within his domain – similar to the "right of first night" allegedly enjoyed by some Medieval Lords and definitely enjoyed by some Ottoman Sultans as late as the 1800s – see here. He would have been unable to make war on Egypt with just his servants he was sojourning with, so, yes, he left it up to HaShem to protect his wife's virtue.
...or, as a humorous aside, maybe he figured he could always get another wife, but couldn't get another sister...