Is lean years the same as poor year?
Your father lived in different times, and he had his share of help.
It seems government subsidies carried him through a number of lean years.

Meaning the government double-crossed him, right?
He got money from the government and that helped him when the times were hard.
No, the opposite. Government subsidies enabled him to keep going (put food on the table, roof over his family's head, etc.) through the lean years.
Yes, same as a poor year. A year of low income---the harvest isn't good, business is slow, etc. I believe the reference is to Joseph's interpretation of Pharoah's dreams in the Bible, of the seven lean cows eating up the seven fat ones (Gen. 41).
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