Spoilers:

Lasombra Antediluvian (or some other extremely powerful Abyssal master/creature) has awoken and is eating his children. The Gehenna Crusade is going poorly, for every 20 lasombra that go to war, 1 returns. The people who will next be asked to sacrifice themselves are the ones looking to defect, and they willing to sacrifice their elders (cardinals specifically) to ensure they are allowed to defect.

Lasombra are also dismayed about how monsterous the Sabbat has become, and how the 2SI is hitting them hard because of the lack of keeping the masquerade.

They are running to the Camarilla because they believe the sabbat LOST. Crushed between the AntiDs and the 2SI. The choice is between pride and death, and the Lasombra are NOT proud, they are pragmatists.

Now, saying this... the Lasombra aren't necessarily correct about the sabbat losing to the AntiDs, nor is the Camarilla necessarily the best choice for protection against either the 2SI or the AntiDs. But it's what the Lasombra feel is best.