Akademik

throw in one's lot with
JOIN FORCES WITH, join up with, form an alliance with, ally with, align oneself with, link up with, make common cause with.
lot

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phrasal
: to join as an associate : share the fate of

reluctant to throw in their lot with a new society — Farmer's Weekly (South Africa)

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throw in one's lot with
To choose to share the fortunes of
lot

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I
decide to ally oneself closely with and share the fate of (a person or group)
II
see lot

Useful english dictionary. 2012.