The Dodgers seem like they're back in the NLCS after an impressive Game 3 win. It looks like a relatively close series at this point, but the Dodgers still have an incredibly uphill climb. If they lose tonight, they'll be down 3 games to 1. The Cardinals blew a 3-1 lead last year to the Giants, getting outscored 20-1 in the final 3 years. It could happen again, but it is much less likely because the Cardinals would have the final 2 games at home this time.
Dodgers - Must Win Games
Game 4 - Only 5 teams since 1926 have come back from a 3-1 deficit to close a series out on the road (1958 Yankees, 1968 Tigers, 1985 Royals, 2003 Marlins, 2004 Red Sox). It is incredibly rare and unlikely to happen against the Cardinals, who have always been especially tough in winner-take-all games at home, except in 1968 (2011 WS, 2004 NLCS, 1987 NLCS, 1982 WS, 1964 WS, 1946 WS, 1931 WS). Yes, the Dodgers have Kershaw and Greinke going again, but it is hard to imagine them hitting enough to win 3 straight elimination games.
Game 5 - If they win Game 4, it won't mean very much unless they win game 5 as well. How many teams have lost Game 5 at home and still won a 7 game series? Only 4: 1926 Cardinals (WS); 1934 Cardinals (WS); 1952 Yankees (WS); 1991 Braves (NLCS). It is even more rare than coming back from 3-1, possibly because of the momentum shift from losing Game 5.
Game 6: If they can win Games 4 and 5 at home, they'll have a chance to close it out in Game 6. This would be the first time that they are in a comfortable spot since the very beginning of the series. Teams close out in Game 6 on the road all the time in the LCS. It has happened 10 times since the LCS expanded to 7 games in 1985 and 3 times in the World Series since 1979 (1981, 1992, 2003).
Game 7: This is obviously a must-win for the Dodgers, and for the Cardinals. This would be an exceptionally difficult game for the Dodgers to win under any circumstance, especially if they lose game 6. Since 1975, there have been 15 times where a home team has won Game 6 to force a Game 7, and the home team has gone one to win 14 out of 15 (only exception: 2006 Cardinals in NLCS).
How many times has a team close the first 2 games on the road and come back to win in 6? 1978 Yankees (WS); 1981 Dodgers (WS); 1985 Cardinals (NLCS).
The Dodgers won 42 out of 50 games at one point this season, so it is not out of the realm of possibility that they would still win this series. They could easily win the next 2 games at home and return to St. Louis with a 3-2 lead, but they have no margin for error. Teams have been winning plenty of winner-take-all games in the LDS, but it is still very rare in a 7 game series.