The only possible reason to “fix” an axle before winter as a reason, is a CV boot has torn and the grease has leaked out. A blast of road salt, and there’s no solution for that axle. Replacement would be necessary. If he caught a torn boot, the boot can be replaced and “fix” the shaft. Once the axle/CV joint starts rattling from salt corrosion, it’s scrap.
Brake lines are a must. If that $450 includes the brake lines and axle, that’s a bargain.
A detailed quote would have really helped. If you are unsure about making auto repair decisions, ASK the mechanic for a written, detailed quote. Post the written quote here.
Thinks OB since the old and rusty brake lines are gone it might not be worth keeping on the road. Again, a written and detailed point would have really helped.