Question

how do we know that the E-field lines are perpendicular to the wire?

Answer 1

otherwise all charges move along the wire and we can not mention about static electric..

Answer 2

E is the gradient of the potential of the wire.
The wire is at a uniform potential locally, and the gradient [thus, E]
is at right angles to this constant potential.

Answer 3

E potential at all points on the surface of a wire is same. E field lines are always perpendicular to an equipotential surface.