Field lines should only provide a visual representation of a field. There is a rule for their construction: take an object subject to a field, move it by d$\mathbf{r}$ and draw the direction of the force due to the field. Do it indefinitely, connect all the d$\mathbf{r}$ and get a line. A field line.
Some examples of common 'properties' of field lines:
The density of field lines is related to the strength of a field.
In plasma physics, there is an effect called flux freezing, where the number of field lines crossing a contour stays constant under topological changes of the contour.
BUT field lines do not occupy a physical position in space so we can draw how many we want?
Does it make sense, then, to talk about the number of field lines?