I did a lot of digging yesterday (ok, I googled "how much health does Lich have in Final Fantasy Origins" and clicked each link until I found one with the information I wanted) and I figured out why Lich didn't die when I did way more than his max health to him. It turns out the people at Square who put out the remakes of the game decided to buff his health along with that of some other bosses. (I did notice Vampire didn't die when he should have but since I just hit him again and he died I didn't pay much attention to it.) So while Lich has 400 health on the NES he has 800 health on the PS and actually has 1200 health on the GBA and PSP. I'm not aware of any changes to the game that would justify this so I assume they just wanted to make it harder. Damage dealt in the PS version is actually substantially lower than damage dealt on the NES as it is, so doubling the health of a monster drastically increases the difficulty of the fight. (Crit percentages were a lot higher on the NES due to a bug and crit damage was a lot higher due to what I believe was a design change and not a bug fix as they fundamentally changed the crit damage formula.)
I'm currently working on leveling to 39 to obtain my 4th attack. My hope is the extra magic defense will help make the slow spell miss and coupled with the 4th attack I should be able to beat him, but I'm running out of ways to get more powerful. There is no 5th attack coming until either I become a ninja (and get a much better weapon) or obtain masamune. There is never a 6th attack. The level cap of 50 means my damage gain from strength, evade from agility, and magic defense from leveling is going to run dry real soon. I was pretty sure I could win with the NES values but can I win with PS values? Who else fatted up? I went into the pages at this site and looked through all the bosses. Most seemed to change between the NES and PSP version but only 6 look to have changed between the NES and PS versions.
Vampire - 156 - 280 - 280
Lich - 400 - 800 - 1200
Kary - 600 - 1200 - 1440
Lich #2 - 500 - 1000 - 2800
Kary #2 - 700 - 1400 - 3200
Chaos - 2000 - 4000 - 20000
Vampire was no problem. Lich hurt but I think I can surmount it. The remaining 4 I'm not sure so sure of. An extra 700 health on the second Kary seems like it might be a real problem but I'm hoping it can be done. 4000 on Chaos is shattering my will to go on. Doing 2000 damage at all was pretty daunting. 4000 seems off the chart, especially with the nerfed crit damage. I'm going to press on, of course, but I no longer feel like this is something I can accomplish. I am now wishing my dead idiots were also thieves so I could kill him with 2 thieves. Instead all my buddies were squishy black mages.
Oh, and Warmech has 1000 health on the NES and 2000 health with a 100 health per round regen rate on the PS. Yikes!