It's not really "lazy" so much as it is taking many of the things that a GM normally does ahead of time - setting up the milieu, putting a plot together, even creating neat NPCs and adversaries - as it is allowing the rest of the players to contribute to this process. As a player I always hated that the DM got to have all of this fun. I realize that it's a lot of work, too, but it's fun work and you should be able to engage in it not just as a co-GM but as a straight-up player. I will say that it requires a bit more out of the players:
Everyone has to have a sense of agency
I guess you could get away with a person or two who is "along for the ride" but by and large you don't want to set up big plots ahead of time. That isn't to say that those kinds of things don't emerge over the course of gameplay, but any crafting of plot has to bear in mind that at the end of the day the players get to dictate what they're doing.
Everyone also has to be on board with role playing
That means, no min-maxing allowed (FATE is kind of too simple to allow much of that, but the pyramid rule of skill advancement does help too), players must play their characters, and above all else the players should understand dramatic irony. That is, there will be lots and lots of times when everyone knows that Dr. Feelgood is a vampire, for example, but their characters don't know and cannot know this. I feel like a good FATE game becomes something very much like a running improvisational drama: losing is an OK thing to do because you should be having fun in ways that don't really have much to do with winning and losing per se.
Those Session 0s are important
Not only is a good Session Zero a great way to kick off a campaign (this is not just where you "roll up" characters but where you all decide on what kind of game you want to play, what tropes you'd like to embrace and which you'd like to avoid, and even maybe sketching out a few of the factions that everyone would like to see in the game), it's good to go back to this every few months to update things, to see where everyone's head is, to review the direction, and so on and so forth. Sometimes those sessions mean temporarily or permanently retiring a character or a party, sometimes they don't, but be prepared for anything.
Understand your role as a GM
It's more to facilitate than anything else. I haven't had a great deal of success using adversaries as players, but there are ways that this can be done for sure, and it does have the advantage that your villains are going to be played by people who want to see their character survive and thrive. At the very least, though, you're probably going to be voicing the more minor NPCs, introducing props, being the final arbiter as to what can and can't be a part of the game, so there is still plenty of work to be done.
Don't be afraid to let people experiment
My immediate thought here is that you can go too far with this, but as with improv I think the ideal you ought to shoot for is when your players ask if they can do X or if Y is an aspect of the game, you try to avoid "no" and find some way to say "yes". I mean, if you're doing a 1980s Diehard type of campaign and one of your players wants to become a Mole Person, that may be something that breaks verisimilitude, but even there, maybe get at what exactly they want to do... do they want to play some kind of underclass in the game whose existence is denied by many? Maybe that can be arranged. For the Y part of things, FATE even has a mechanic wherein a player can spend a FATE point to add said aspect. I would go so far as to not require the spending of these if an aspect doesn't directly aid the party - for instance, if a player just one day has the idea that elves exist in your world but pass for humans, and the party goes along with it, you ought to just allow it rather than make them use up a FATE point.
Lead by example
A lot of players more used to classic RPGs may take some time to get used to the free-wheeling bits of FATE. Try and encourage them if you can. If you don't have a setpiece ready to go for a battle, just straight up ask the party where the battle is taking place and what kinds of things they might encounter there, and build aspects based on that. If your players don't get the "chain aspects together to beat something up", have a big bad do that to them or give them a seemingly insurmountable challenge that requires this. When you do or a player does invoke an aspect, don't just allow them to invoke it, narrate how they're using it (in fact, what I do is I don't allow my players to invoke an aspect, physical or otherwise, unless they can justify it somehow). Make weird characters with weird personal aspects that you then invoke during play to give them more flavor than your average mook. Always have a physical aspect or two on the table whenever there's a fight or a pursuit or practically any kind of die roll. When a player invokes an aspect to win something, invoke one right back on them and narrate how this is happening ("Oh, so you invoked the Burning Oil and you toss Dr. Deepwater into it... but at the last second his Lightning Reflexes kick in and he does a backflip over the water!"). FATE does this thing where some seriously awesome stories just seem to come out of nowhere.
Mostly though, have fun!
The single biggest thing I like about FATE is that it's very rules-light. There are a couple of mechanics that players may take a little while to "get" (chaining aspects seems to be a big one) but mostly there is very, very little room for rules-lawyering. If a player starts to overuse a skill, the way you combat this as a GM is by sometimes throwing obstacles to make it tougher for that player to use it (if he's really good at hand to hand combat, maybe he gets a reputation as such and so every now and then a tough guy chooses to shoot him instead) but at the same time high rolls that result in crazy crap are fun, so bear that in mind. When you go into every session with a general idea of what might happen but no specific "the party must go to X" in mind, it allows for a great amount of free-wheeling fun.
