I've recreated your nodetree to get a similar setup like you have. The reflection is calculated in the frame titled "REFLECTION ON SURFACE".
It is basically doing two things: First evaluating the normal of the target surface which you already had in your nodetree. Next using the Vector Math node set to Reflect to calculate the vector of reflection between the position on the surface and the surface normal, then using this as offset for the Extrude Mesh node instead of the normal in your setup.
Note: Usually I would get the vector of the incoming mesh line by subtracting the position from (0, 0, 0) and then plugging it into the Reflect node. This would result in a vector that needs to be scaled by -1 to get the correct result.
To save some nodes, the scaling wouldn't be necessary if instead of subtracting the position from (0, 0, 0), you could switch those inputs and subtract (0, 0, 0) from the position which is simply the position itself. In this case with the lines' Start Location at (0, 0, 0) it works to get rid of a Subtract and a Scale node.
The "full" setup would look like this:
And this is the result viewed from the side and the top. I've reduced the number of lines to 3 and the Offset Scale on the Extrude Mesh node to 0.5 so that it becomes more cleearly visible which the reflected lines are.