Alright, I've hunted a decent amount of liches and I think it's time I give my two cents on the matter, I'll go ahead and put my TL;DR here, I find the system as a whole frustrating and not terribly rewarding at this point, because of how many separate chances are involved in the grind for them right now, and how failing one chance can make go through the entire loop again, but with a few tweaks (I put a couple suggestions down at the bottom) it could be the sort of thing I enjoy doing regularly.
Now, for context as to what my rewards have been so far...
1 converted Lich-bro with the Chakkhurr, nice to see him pop up, just wish he was more efficient considering how infrequent his visits are.
2 Kuva Drakgoons, pretty enjoyable, feels like a decent upgrade to the drakgoon, both of my rolls had good bonuses, with the second being an upgrade to the first.
1 Kuva Shildeg, feels like a decent weapon, but hammers aren't my thing, looks pretty though.
1 Kuva Seer, It was dreadful, I had a bad element for my bonus(I know how to influence the element, I just wanted to experience all the different types of liches), and it just did not feel fun, even after 5 Forma and a bit of experimenting, between the high zoom, the projectile having travel-time, the low ammo reserves, and the awful fire-rate and reload speed, I just wanted it gone.
1 Kuva Twin Stubba, decent elemental bonus, okay predecessor to the Stubba, was really sad to see that it wasn't compatible with my Stubba riven though, I kinda thought since the update note only mentioned that 3 of the weapons were "new" maybe it would've worked, despite other "dual sidearms" having the same issue, but oh well.
1 Kuva Tonkor and 1 Kuva Ogris, both of which feel solid, though I don't have much experience with the predecessors, and I haven't put too much work into them.
1 Kuva Chakkhurr, looks like a sniper, feels like a sniper, but the mod screen says it isn't a sniper, and because of that it just doesn't feel right to me, this was the one I most recently got, and I haven't put any Forma into it yet, but it just feels like another weapon I'm gonna have to waste mod slots on to bring Fire-rate and reload speed up to a decent level, it just doesn't feel like it really fits into this game of hordes.
1 Ephemera, it's pretty, was really happy when I saw my lich was on fire.
Now, onto the fun part, why does the lich system as a whole feel so off-putting? Personally it's because I feel like I waste most of the time I grind, I grind for relics, I get the wrong relics, because the liches I've slain formed a pact and decided they wanted to die to Vome, and Ris, and Fass, I grind more relics, I finally get the one I need, I throw traces at it, I get the common drop, back to step one, this time after refining it I get an uncommon but it's the wrong one, back to step one, oh wait, I'm low on traces, gotta grind more of those now for that better chance, I have traces and the relic I need now, I run it again, oh good I get the mod I need to end my current lich, but that exhausts another mod, and my dread grows, what I'm trying to say is, chance-for-chance is frustrating, unrewarding, and makes the time I spend getting those chances, time I regret because it just doesn't work out, over, over, and over again, now add on to that getting liches who have things you literally don't want at all and it would feel... just, crushing.
So, how does this system get less frustrating? Choice. Make it so relic rolls for common and uncommon tiers allow the player to choose what reward they get(or allow us to deconstruct rewards we don't want into tickets based on the relic we cracked open so we can trade those in for something we want when we grind enough) make getting the relics in general is more reliable via a choice at the end if one was going to be awarded, with those two tweaks the system sounds a lot better to me, I get that you don't want players to be able to just rush through the content you work hard on, and I understand if you don't think these changes are the right way to go, thanks for reading, thanks for the work you've put into the game so far, and I hope you have a nice day/night.