The X-Men Animated Series that aired in the early '90s altered the background of Deathstrike so that she and Wolverine were once lovers. This, however (like a ton of other things in the animated series), is not accurate to the comics.
Also, Wolverine didn't kill Deathstrike's creator. He killed her father, who (in the comics) was the creator of the adamantium bonding process. Deathstrike was altered to being a cyborg by Spiral and later enhanced by a man named Pierce (a former member of the Hellfire Club), who is the leader of the cybernetically-enhanced mutant group called the Reavers.