Why team lairs are a bad idea
Teams are more of a hero thing than a villain thing. Most heroes all want the same thing (justice, victory over some bad guys, whatever) and they all equally benefit by doing their thing. Most villains have competing goals, or want things that must be divided among them (money, commodities, whatever). This makes villain teams more volatile than hero teams, all things considered. Jealousy, greed, and selfishness aren't unique to villains, but our endgame makes us more vulnerable to those feelings.
If your team collapses, you've got a bitter ex-member or three who can report where you hang out to the cops, or your heroic nemesis. And then you're stuck. If any of your nemeses find a shared lair, your entire villain team is out of options. Even if the discovery is entirely accidental, or due to detective work by somebody rather than betrayal, everyone bears the risk.
When team lairs are a good idea
Team lairs are a good idea in the following circumstances.
- Your team includes one or more people who can create lairs in hostile or inaccessible locations - in a volcano, underwater, or very deep underground for example. This strongly mitigates the risk of discovery and destruction. The downside is that you're usually beholden to those people for lair maintenance, and stocking it can be a pain in the ass.
- Your team is mainly junior-league villains, or apprentice villains, and you are mentoring them. In this case, you want to keep an eye on them during their downtime, you want training facilities, yadda yadda. The risk here is that one or more of them will accidentally lead the heroes back to your lair. You can mitigate this risk by always traveling as a group. You'll want a security system that lets you monitor entrances and exits, but hey, you signed on for this if you took on mentorship duties. Suck it up.
- Your team is cooperative, and explicitly has a profit-sharing arrangement or is after some intangible reward like revenge. If the issues of betrayal aren't a factor for your team, then there's no reason not to build a shared lair. In fact, it can be to your advantage.
Team lairs aren't built differently from individual lairs in principle. You obviously need living space for each member of your team. Be sure to build a couple of extra rooms, in case the team grows for some reason.
Team lairs frequently have higher security requirements than an ordinary lair. You should always factor a security system into your building plans, and sketch out how it works and what it will cover before you start construction.
Team lair roles & responsibilities
A team lair should have a designated landlord. This is the person with final authority over the lair, its occupants, and its contents. If your team has a leader or senior villain, he's usually it by default. If your team has only one person whose powers make your lair possible, that person should be it.
There's two other roles, some or all of which could be done by the same person: quartermaster and security chief.
The quartermaster is responsible for obtaining lair furnishings, accessories, food, and other supplies. This is the person with the civilian identity, teleportation powers, or whatever makes this job easiest. The reason to have a quartermaster is that any interaction you have with the mundane world is based on two things: cash, and lies. Cash is easy to obtain, but keeping track of the lies you tell to keep people from getting suspicious about your lair is difficult for multiple people to coordinate.
The security chief is responsible for, obviously, lair security. He or she gets to control comings and goings. You do not let someone into the lair without this person's consent. The security chief is also on the hook for any cameras, security sensors, or whatever else the lair might use for access control and monitoring.
Maybe your team doesn't roll with the idea of "senior members" or delegating authority. That's fine - all I can do is tell you what is known to work within the villain community. Each villain is unique, meaning each team is as well. Ultimately you have to do what works best for you.