Yes they are distorted. The simplest example is a static point charge in a modest gravitational field. Then we can calculate the electric field by using the fact that it is the same as the field observed in an inertial frame for a charge undergoing motion at constant proper acceleration relative to that frame. This can be calculated using Maxwell's equations in flat spacetime. Here it is:

[![Picture of electric field lines for charge undergoing motion at constant proper acceleration][1]][1]

This image shows the electric field for a charge undergoing motion at constant proper acceleration in the upward direction, in flat spacetime, as observed in the inertial frame where the charge is momentarily at rest. At this moment the B field is zero. The same image also shows the electric field for a charge held at a fixed position in a modest gravitational field directed in the downwards direction on the diagram.

Thus we can observe the easily-remembered fact that gravity causes the field lines to "droop". [1]: https://i.sstatic.net/8kfmh.png

Yes they are distorted. The simplest example is a static point charge in a modest gravitational field. Then we can calculate the electric field by using the fact that it is the same as the field observed in an inertial frame for a charge undergoing motion at constant proper acceleration relative to that frame. This can be calculated using Maxwell's equations in flat spacetime. Here it is:

This image shows the electric field for a charge undergoing motion at constant proper acceleration in the upward direction, in flat spacetime, as observed in the inertial frame where the charge is momentarily at rest. At this moment the B field is zero. The same image also shows the electric field for a charge held at a fixed position in a modest gravitational field directed in the downwards direction on the diagram.

Thus we can observe the easily-remembered fact that gravity causes the field lines to "droop".