No, a turn before a flip is not required, and there can be turns before lutzes.
The defining characteristic of a lutz is that the skater is on a back outside edge traveling in the opposite direction, on the opposite foot, from her standard landing edge and reverses the direction (clockwise to counterclockwise or vice versa) at the moment of takeoff.
With a flip, the skater is never traveling in that opposite direction.
With a flutz, the skater starts with the upper body check and direction of travel opposite to the in-air rotation but releases it too soon, before getting off the toepick and into the air. It's a flaw, especially if it happens before the toepick even goes into the ice and the edge change is severe, but the intention is clear.
If the prerelease of the check is minor and just a small fraction of a second before the pick leaves the ice, the edge on the other foot might be flat or very shallowly inside at the instant of takeoff, but since most of the weight is on the picking foot at that point that small edge change doesn't really change the nature of the jump.
Sometimes with jumps out of footwork the last step does not end up on the edge that the skater wants it to be on at all, because of too much or not enough upper body check at the exit of the turn or when the blade steps down onto the ice,, then it might be ambiguous what the skater intended. This is much rarer. In those rare cases the tech panel might need extra time debate what jump they think the skater was doing and might need to refer after the fact to what other flip- or lutz-like jumps were performed in the program to try to guess the intention.
If the tech panel had to decide whether to reclassify an obviously intended lutz as a flip or vice versa every time there was a subtle edge change, the process of reviewing jumps would take a lot longer and slow down the wait for the marks. It's much quicker just to call the "e" and let the judges penalize the GOE as they see fit. It also penalizes otherwise good jumps only 1 point or so for a slight flaw, instead of causing a skater to lose 6 whole points if the tech panel identifies three of the same jump.