GA Flight Instructor with student reported an NMAC while on the approach pattern of LAF airport requiring evasive action to avoid a collision.

Narrative

For a training flight with a student; I was told when 10 miles out by LAF Tower to report 3 miles north for right traffic Runway 28. When reporting 3 miles north; Tower gave an amendment to my instructions and switched me over to the left downwind for Runway 5. This was simple enough as it required a standard 45 degree entry into the left downwind. As we approached 2 miles; Tower gave instructions to Aircraft Y to take off of Runway 28 which was full length. As we entered the left downwind for 5; we spotted Aircraft Y on the upwind of 28 which directly crosses into the left downwind of Runway 5. As it became apparent that the aircraft's good climb rate would have resulted in a near midair collision; I assumed the controls from the student and executed an immediate right 360 turn to avoid the aircraft which was on a perpendicular collision course. I stated to Tower we were taking evasive action and making a right 360 for collision avoidance. In the right 360; Tower then switched Aircraft Y to left traffic Runway 5; which in turn placed them in sequence before us to land. Once established on the downwind we resumed normal operations and landed without incident. Tower never acknowledged the risk of having an aircraft taking off on a crossing runway to us.