Can 2 circle and 3 lines get 17 intersection points?

Yes.

Draw three line segments so that they cross at three points forming a triangle (with each side extending beyond the vertices of the triangle).

Draw one circle to enclose the triangle without touching it to intersect the extended sides at a further 6 points, making 9 points of intersection so far.

Draw the second circle slightly shifted (relative to the first) so that it also encloses the triangle (without touching it) creating a further 6 intersection points with the three lines and 2 with the first circle; an additional 8 intersection points making 17 in all.