throw in one's lot with

/TH R OW1 IH0 N W AH0 N EH0 S L AA0 T W IH0 DH/
verb
  1. 1

    To join with; to share the fortunes of (a person or group).

Source: https://en.wiktionary.org/wiki/cast%20in%20one's%20lot%20with, https://en.wiktionary.org/wiki/throw%20in%20one's%20lot%20with