Solution found with 3 lines.
Line 1 starts at (1,0)
  goes through (1,0) (4,4) 
  and ends at (4,4)
Line 2 starts at (4,4)
  goes through (2,1) (4,4) 
  and ends at (2,1)
Line 3 starts at (2,1)
  goes through (2,1) (4,0) 
  and ends at (4,0)

1 solutions found.