Fack Youk looked at this issue a bit in 2009. See Jeter, Gehrig, And Home/Road Splits. It does not seem like they got into too much detail, perhaps because of data limitations that may no longer be a problem.
The table below shows how Gehrig and the AL did from 1925-1938 (so not quite all of his career). H means home games and A means away games. Some data was from Retrosheet and some from Baseball Reference.
It is pretty clear that AL batters from 1925-38 hit better at home. Their AVG was 14 points higher at home while Gehrig's was 22 lower. So that is a swing of 36 points. The swing for SLG was 47 points.
This next table shows Gehrig compared to the top 10 Yankee left-handed batters over this period. I used BB% here instead of OBP (BB/(AB + BB)). Who those 10 guys were is listed at the end of this post
It is pretty clear that those other Yankee lefties did better at home (except in batting average on balls in play (BABIP)). But even there Gehrig had a bigger difference, .033 vs. .012. This just about explains his lower AVG, SLG, OBP at home. Notice his ISO (SLG - AVG) is just about the same, home and away. The other Yankee lefties did much better in ISO at home.
Maybe Gehrig was more of a line drive hitter, so he did not get as many HRs into the short rightfield porch as we might have expected. That would also explain why he got hurt even more on BABIP. If the right fielder is playing in closer, he catches more of those line drives and your BABIP suffers.
Here are the top 10 Yankee lefties in PAs from 1925-1938 not counting Gehrig (I also removed Lefty Gomez, since he was a pitcher). These guys collectively had about 12,900 PAs at home and about 14,000 PAs in away games.
Earle Combs 6470Babe Ruth 6013
Bill Dickey 4939
Red Rolfe 3115
George Selkirk 2025
Joe Sewell 1754
Tommy Henrich 817
Jack Saltzgaver 760
Gene Robertson 623
Cedric Durst 529
Here is what they each did, home and away