+1 do not replace solid lines with any sort of flexible.
The previous owners must never have changed their brake fluid resulting in your lines rusting. Since brake fluid absorbs water over time or breaks down into water and it's other components when overheated, you will get rusted lines from having the water in the lines and well you're also in a marine enviroment.
For street driving most manufactures recommend the fluid be flushed out every 2 years, if your autocrossing it you should change it out at least once a year, road coursing the car I'd check after every event.