No it's not possible for electric field lines to cross.
So no electric field lines cannot cross each other.
Electric field lines are basically a visualization of the electrical vector field and at each point, the direction (tangent) of the field line is in the direction of the electric field.
Also at each point in space (in the absence of any charge), the electric field has a single direction, whereas crossing field lines would somehow indicate the electric field pointing in two directions at once in the same location.
Field lines sorta of do cross, or at least intersect, in the sense that they converge on charge.
If there is a location with charge, the field lines will converge on that point.
However we typically say the field lines terminate on the charge rather than crossing there.