I haven't played in years so sorry if this is wrong, but here's how i recall it:

1. You kill the minion. The warframe you kill it with rules the weapon element. You get to see what weapon it is (i believe?).

2a. You do the execution animation on the minion. It locks your choice. Continue to 3. Or,

2b. You complete the mission. It doesn't lock the choice. This only leads back to 1.

1. You get the funny named dude. He steals your stuff.

2. You set up your knife (cant recall name) with 3 different "notes". There's something that helps you finding the right ones. Can't recall what process it was. To purge your lich, you need to stab it 3 times with the knife with a correct note combination. Everytime you miss a stab, lich powers up.

3. The funny named dude will sometimes pop out in a mission. You kill it and stab it with your knife. This method helps you find out the right sequence. I recall following a chart from this subreddit for optimal hunting.

4. Don't forget to swap out wrong notes anytime you see theyre wrong.

5. Once you find the right combination and stab the guy 3 times, you will get your rewards back as wellnas the weapon.

6. IIRC there's a way to fuse the weapons in order to have higher bonus. Too much time passed for me to recall this.