バッテリーパックの寿命です fully qualifies as a main clause of this sentence. Its subject, which is omitted, is それ, vaguely referring to the situation previously mentioned. Subjects are omitted all the time in Japanese sentences, and there is nothing special in this case. Technically, the last half of this sentence is not a noun clause, because it has no nominalizer and ends with です, a copula (aka linking verb).
寿命 in this context is end-of-life rather than lifespan. 寿命だ／寿命です does not mean "It's a lifespan" here, but it means "is reaching / has reached the end of one's life," "is near one's end," "is dying a natural death," "is on one's last legs," etc.
In other words, 寿命 is sometimes used as a no-adjective, usually in combination with もう.
The watch has reached the end of its life (and thus not repairable).
- また止まったの？ それは時計の寿命だよ。
It stopped again? That means the watch has reached the end of its life.
- もう寿命のスマートフォン a smartphone near the end of its life / on its last legs