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No, these are two separate anatomic areas, and it is not likely that one would be directly related to another.
Certainly, if the ankle injury caused you to trip and fall, and then injure your back - then yes, they could be related.
But in the general sense - an injury at the ankle would not be responsible for degenerative changes in the lumbar spine, and would not be a cause for "ruptured" discs.
my left ankle was 1st injured in 1986 inthe militay, sinced then it has flared up on numerous occasions, in 2008 i reinjured it again and it was in bad shape for about 16 months straight. during this time i was not walking correctly, had a limp and had pain in rt knee and lower back.. shortly after i fell due to ankle being unstabe and had 3 ruptuerd discs in lower back.
Well, if you fell, perhaps that had something to do with the flareup of back pain.
But in general, the ankle injury would not be directly related to a back injury. Even if you were not walking correctly for a short period of time, this generally would not cause severe degenerative changes in the lower back.
Of course, it is hard to make general statements, because everyone is different, but I would say your back issues are independent of the ankle issues.