The height of an image formed by a lens is

An object is always kept above the principal axis and the distance measured above the principal axis is taken as positive.

A real image is always inverted and as such, the distance measured below the principal axis is taken as negative.
A virtual image is always erect and as such, the distance measured above the principal axis is taken as positive.

Since a lens can form both real and virtual image, depending upon the type of lens, the image height is either positive or negative depending upon the nature of the image formed by the lens.