It's important (in my opinion) to build your deck engine around your commander. If I were designing a deck around the commanders you've mentioned, here's what I'd do. I know this isn't specifically what you asked, but drawing more cards is a key part of Commander strategy.
Lyzolda
Well, she has card draw built in to her. Look for cards that will give you black or red creature tokens (and ideally both, but there's only a couple of those). Also look for ones that are either permanent token generators or can be re-cast from the graveyard. Some examples:
As supporting cards, black has many instants and sorceries for drawing cards and for searching for specific cards. There's no need to have all of your non-land cards have the same mechanic (in fact, that would be a poorly balanced deck).
Uril
Obviously, it's key to get Auras onto Uril. Thankfully, White and Green have cards that help you if are playing something Aura-heavy.
- Verduran Enchantress, Mesa Enchantress, Argothian Enchantress, Enchantress's Presence: all give you card draw when you cast an enchantment
- Green Sun's Zenith, Chord of Calling, Worldly Tutor, Summoner's Pact, Fauna Shaman: all let you search for creatures
- Academy Rector, Enduring Ideal, Enlightened Tutor, Idyllic Tutor: all let you search for enchantments (Enduring Ideal is a bit of a weird one though!)
There's also a bunch of creatures with the word "aura" in their description that do cool stuff. Pick all your favorites and your favorite auras and have fun.
Lovisa
Mono-colored commander decks are a little trickier. Every color has some way of drawing more cards, so you generally have to rely on that. In red's case, you are usually (but not always) "looting", i.e. discarding either before or after you draw. As another poster mentions, artifact draw can also help.
Hope this helps.