Let's say that the B-26 LBJ was on really did come under Japanese fire. There are some like Robert Caro who still believe it did--but even if in fact the plane's generator problems forced it to turn back before engaging the enemy, let's assume (1) that it doesn't have those problems, or (2) that LBJ gets on another B-26 ("Lt. Col. Francis Stevens died in the one B-26 that was shot down that day. In a twist of fate, Johnson originally had boarded that B-26. After a bathroom break, Johnson got on a different plane nicknamed the 'Heckling Hare.'"
https://web.archive.org/web/2008061...2001/johnson.silver.star/story/storypage.html) Anyway, LBJ is killed. Consequences? Senator Coke Stevenson? No Civil Rights Act of 1957? A race between JFK-Symington and Nixon-Lodge in 1960?
Well per Robert Caro in Master of the Senate, Johnson was instrumental in blocking an attempt in 1957 by Richard Nixon and several of the leading liberal Democrats (Paul Douglas, Hubert Humphrey, and Clinton Anderson) to abolish the filibuster.
Apparently the plan was that at the opening session of the 85th Congress, Anderson would make a motion to adopt rules for the new Senate, Douglas would then request a ruling from Vice President Nixon (acting as President of the Senate) on whether Anderson's motion was in order and also about what rules the Senate was operating under, and Nixon would then rule that the motion was in order and that at the moment the Senate was operating under standard parliamentary rules since the Senate was not a continuing body whose rules carried over from session to session. Such a ruling would mean that there was no filibuster in effect (since under standard parliamentary rules only a majority is required), and thus the filibuster would be dead unless a majority of the Senate voted to include it in the rules that would be adopted for the 85th Congress. (Which the Republicans and liberal Democrats would then oppose.) Johnson was apparently able to use his position as Majority Leader to get the Anderson motion tabled before Douglas was able to request a ruling from Nixon thus killing the attempt to block the filibuster.
If there is no Majority Leader Johnson than it is possible that the Democrats might have a majority leader who is not so closely aligned with the Southern Democrats and who allows Douglas to make his request for a ruling on the Anderson motion. And if the filibuster ultimately gets removed then it is very possible that a strong civil rights bill passed in the 85th Congress. (Both Nixon and Senate Minority Leader William Knowland wanted to see civil rights legislation passed that year, so they would probably be able to get enough Republicans on board to establish a pro-civil rights majority with the liberal Democrats.)