Replace fiber sheathing on 1940's house while re-siding? – GreenBuildingAdvisor

We are slowly renovating a 1949 single level 1300 sf house we own in a working class neighborhood in a small city in Virginia, northern edge of CZ 4A.

The house has aluminum siding over the original wood lap siding and our next project is to remove both layers and add continuous insulation and fiber cement lap siding. 

The sheathing underneath is (probably 1940’s) fiberboard over 2×4 framing. 

Thoughts on leaving this sheathing as-is if it is in good condition, replacing it all, or adding sheathing over the existing?  

Thanks