Good to see people are interested in the game being picked back up. While I understand the game in abandonded, it still feels a bit iffy continuing someone elses work. I'm currently in the process of replaying the game thoroughly and making notes on notable things from the story. I have a lot of thinking to do but would love to know what everyone else thinks just so I can gather a consensus on how best to move forward.
I would recommend trying to reach out to the original dev as they might give you permission but more importantly, they may also give you some direction on how they expected to develop the game, or even better some kind of design plan, assets and files.
Without this, picking up the game could prove quite hard: it's an old game, probably using old versions of softwares and someone else's code. You could also trigger some harassment from fans or people saying it's not real work and you shouldn't be paid for it (unless it's an official agreement for example)
From my point of view, if you can get an agreement from the original dev (or buy from him the rights) to use the assets, then it's easier to pick the game where he left it. Otherwise, it's probably way easier to just start over with your own code, your own ideas. Mention the game is inspired by Lust Man Standing by Endless Taboo and try to stick to a V1 close to the existing content so people can actually compare and decide if it's worth following to "replace" it.
Having your own game makes it easier not only from a development POV, it's also easier to advertize and if you plan on being serious about it, man it's worth the hassle when the fanbase comes for YOUR work and not because you used existing stuff.
If you can create assets (meaning characters, design etc.) close to Lust Man Standing with a similar-sounding story, it should work. Feel free to explore your own ideas for the scenario, you have a great story to start with, I'm sure it will inspire you to write more