To determine if lines are parallel, perpendicular or neither, we need o determine each line's slope.
If slopes are equals then they are parallel.
Let us calculate L1 slope (m1)
m1= (y2-y1)/(x2-x1) = (4-4)/(0+1)= 0
slope 0 means that the line L1 is horizontal or parallel to the x-axis.
Now the slope for L2 (m2):
m2= (y2-y1)/(x2-x1)= (2-6)/(5-5)= -4/0 Undefined slope
Undefined slopes means that the line L2 is vertical or parallel with y-axis
Then the lines L1 and L2 are perpendicular.