In terms of plans, scamming should work very well in combination with the direct approach, particularly if combined with a Mastermind Point. That's because if we get leverage over the local Cultivators we don't have to exploit them for money, we can also pump them for information or get them to betray their sect in ever escalating ways. This would hopefully give us a way in, or at least a lever to make one.
The basic plan would be to take inspiration from Nameless' memories of how organised crime rings were rolled up back on Earth. He starts with a junior member of the organisation and compromises them, and so flips them. Using what he learns from there, he can work his way up the chain until he gets to people who know useful things and have actual influence. In this way he can start to subvert the operations of the sect itself. Even better though, there are three rival sects in the city, and he can work on all of them at once, building the tension between them that will already be elevated by one of the Patriarchs ascending to the Reality Forming stage, and the threat that he's going to get even stronger with whatever he's found. He can exploit that to cover up his own activities, to cause distractions, or even to set up situations where his catspaws succeed and so are given more responsibility. His Potentiation boosted illusions really pay off here, as he can impersonate members of the sects to one another to stir tensions or manufacture conspiracies. Additionally, normally sects would be too static for this kind of subversion to happen quickly enough, but the situation will be in complete flux at the moment, and we can use that.
For example, one way of playing this is to substantially weaken the Bleak Raven sect, so that they get desperate enough to accept Nameless' offer of aids at a critical point to tide them over until their Patriarch emerges from seclusion.
This is why spending a Mastermind point on scamming is so useful, because it does a lot more than give him resources, it also means that his direct approach to the lich question will have a huge amount of potential backing if we make proper use of it. Stripping the locals of their Treasures will also probably make them more desperate and destabilise the situation any more, allowing Nameless and Xiaoling to compound their scamming.
This may also setup a giant scam, where we frame the sect as being in collusion with a Diagram Lich (whether or not they are), which would allow for some industrial grade exploitation and so very rapid cultivation for a while afterwards. This is where being able to cast illusions and the hidden ability to cast Diagram spells comes in very handy, as he can do things like impersonate the lich and have him be caught conspiring with a Sect Elder.
One of the reasons we went with Xiaoling was for the social benefits she brought, so lets try it out and see how it works. Spending a Mastermind point on this is there fore efficient as there's more to leverage. And don't tell me that the combination of the near supernaturally beautiful innocent young daughter of a Great Clan and Nameless can't come up with some amazing scams to work on the stereotypical xianxia characters. How many times do you think that Nameless would have to broker a deal or come to her rescue after some arrogant young inner disciple or lecherous sect elder implies ambitions on her virtue.
We should remember our father's teachings, both how to enslave and when not to, but also this:
The nameless heir soon learned that the ideal strategy was to play a myriad of simple plans, each of which could pay out substantially if successful, but whose loss would not be critical in the grand scheme of things. One took credit for the plans that succeeded, brushed the others under the table, and used the reputation gained thereby to support wilder schemes.
We shouldn't only have one plan in motion at a time. We shouldn't only be depending on what we can get from the lich, we should have backup plans like extorting the local sects based on our knowledge of his presence if that doesn't pan out.
In my opinion it's pretty likely that Bleak Ravens are minions of this lich. Weakened core sounds like a thing that allows for subversion by Alvan's Crown of Tragedy especially if Diagramist have a Beyond version of spell. Hell, maybe he deliberately arranged things so that sect is vulnerable to this and now they're protecting their boss from big scary Nameless and his Ring of Doom. Or maybe lich plans to pull voluntary soultheft or something similar on that Patriarch and dodge the Doom that way, there is probably spell for doing that.
How would the lich know about Nameless or his Doom though? We were told that none of the other liches dared look at Fate.
The mind control option looks plausible, if unlikely. If the lich has been pulling the strings of the sect, then it may have developed Cultivation boosting spells, such as a force grand diagram that makes a place better to cultivate in. It still seems like a long shot though.