In the case of the baddies I think there are two specific reasons why they may not have bothered with Felix Felicis.
The first might be a certain hubris. It's impossible to examine each Death Eater individually, but Tom Riddle in particular was very arrogant and very confident in his abilities.
'I fashioned myself a new name, a name I knew wizards everywhere would one day fear to speak, when I had become the greatest sorcerer in the world!'
Harry Potter and the Chamber of Secrets - p.231 - Bloomsbury - Chapter 17, The Heir of Slytherin
Consider also the supreme confidence Bellatrix displays in herself in her final fight:
'What will happen to your children when I've killed you?' taunted Bellatrix, as mad as her master, capering as Molly's curses danced around her. 'When Mummy's gone the same way as Freddie?'
Bellatrix's gloating smile froze [...]
Harry Potter and the Deathly Hallows - p.590 - Bloomsbury - Chapter 36, The Flaw in the Plan
I always got an impression of great pride from the higher-ups among the Death Eaters, possibly something that their Pure-Blood supremacism contributed to. It displays a certain humility - even a lack of faith in oneself - to depend on luck.
This is a minor point though. I think the major point is the Death Eaters, and particularly Voldemort, believe in Dark Magic.
'The old argument,' he said softly. 'But nothing I have seen in the world has supported your famous pronouncements that love is more powerful than my kind of magic, Dumbledore.'
Harry Potter and the Half-Blood Prince - p.415 - Bloomsbury - Chapter 20, Lord Voldemort's Request
This, I think, is very important. Don't you think lucky potion is a bit friendly? It may very well be amoral, but it's not poison and venom and hatred and fury. It's a bit well-meaning. A bit soft and fluffy. A bit nice. It may not be love. It may not be Dumbledore's kind of magic. But it's not really Voldemort's kind of magic.
Bellatrix beat me to one of the juicier quotes, as is her nature :P but permit to restate the point in combination with another, for I think both are needed to make the case.
Consider these two pronouncements together. First Hermione:
'Luck can only get you so far, Harry. The situation with Slughorn was different; you always had the ability to persuade him, you just needed to tweak the circumstances a bit. Luck isn’t enough to get you through a powerful enchantment, though.'
Harry Potter and the Half-Blood Prince - p.484 - Bloomsbury - Chapter 24, Sectumsempra
And, second, Slughorn:
'Because if taken in excess, it causes giddiness, recklessness and dangerous overconfidence,' said Slughorn. 'Too much of a good thing, you know ... highly toxic in large quantities. But taken sparingly, and very occasionally ...'
'Now, I must give you warning that Felix Felicis is a banned substance in organised competitions ... sporting events, for instance, examinations or elections. So the winner is to use it on an ordinary day only ... and watch how that ordinary day becomes extraordinary!'
Harry Potter and the Half-Blood Prince - p.178 - Bloomsbury - Chapter 9, The Half-Blood Prince
And this I think is the point of it. The wisdom within the wizarding world - the kind of thing surely someone like Dumbledore or McGonagall would ascribe to - is that Felix Felicis works best on an ordinary day. It works best at making something ordinary extraordinary.
Consider, luck cannot give you powers you don't already have. What it's good at is giving you confidence, lighting your path, making things work out, letting you run into the right people, making sure you don't face a locked door, helping your confidence, helping you make that save by a few millimetres instead of missing it by a few. It's a boost.
Now, having said that, we do see that the DA did use it in a battle situation and it does seem to have helped keep them alive. (However, with all such things as hand-wavey as "luck", one has to question just how lucky Ginny got that night given how her brother was brutally savaged by a werewolf).
'Harry, if we hadn't had your Felix potion, I think we'd all have been killed, but everything seemed to just miss us -'
Harry Potter and the Half-Blood Prince - p.571 - Bloomsbury - Chapter 29, The Phoenix Lament
Nevertheless, wisdom suggests great caution. As I say, liquid luck cannot give you additional powers. Now ask yourself whether it is really such a good idea for the person who believes they cannot be hit to stride confidently into battle against a stronger opposition. Who knows what kinds of horrible situations they might walk brazenly into, lacking precisely the kind of caution and fear that they might need. Of course, Felix should stop them, or put something in their path, perhaps, make sure that door is locked this time. But I think the wise path is to study and improve and better yourself so that you aren't reliant upon lucky potion, perhaps especially for something so important as a big mission. The dangers of overconfidence mixing with incompetence are ghastly and the risks of the potion running out when you're still in the mess that the lucky potion had been helping you survive are worrisome.
Other answers have touched on this, but for everyone, I think the fog of war makes having Felix around when you need it quite difficult practically too. On the Death Eater side, I think it would be hard for anyone but Voldemort to know when the next big operation is gonna be sufficiently far in advance. Dumbledore too wouldn't have known precisely when he was gonna make his next major breakthrough. Now we know from the books that Harry's phial of Felix lasts much of the school year, so it can't perish that quickly, but if we allow ourselves to assume it has a best before date, it must be tricky to ensure it's there when you need it. And what do you do when you've taken it all?
Moreover, what if it turns out that, despite (or maybe because of) your luck, this operation didn't quite turn out to be the big deal you expected. How do you know in advance whether this is the big one? And, with that in mind, how do you stop yourself depending on it? How do you know in advance whether this isn't the big one? How do you stop yourself wasting it. What if you don't take the Felix and then, since you haven't had your lucky potion, you wind up in a really big mess where this time you really do need the lucky potion. I suppose you could carry it around constantly, but it might be a bit late when you're already magically bound and gagged and really in need of a stroke of luck.