What places can Lifs be found?
How strong are they?
Maybe it's just because it's late and I'm tired, but the previous post seems to be quite unclear.
There is no monster named "Lif" roaming around on any map. I believe my foreposter was trying to be funny (hahalol~nyo^^) saying they can be everywhere (yeah, because players can summon them anywhere), but you don't capture them, and you won't have a monster egg.

Homunculus (Lif, Amistr, Vanil, Filir) and tamed pets (Poring, Poporing, Munak, Bongun, Alice, Zealotus, Bapho Jr., ...) are quite different.
The thing you're refering to are tamed pets - those you catch with the taming items like eimi said, and you can hatch them with an egg incubator. They won't help you, they won't level, but they'll spam emoticons, and if you get them to loyal, they'll "talk" (basically say a few phrases that are different to every tamed monster). Oh, and you can make them do a performance by right clicking them and selecting "Performance" - they'll then do a little animation (like a Bapho Jr will drink beer X3). They cannot die, and if you get killed, they'll do "/
omg" or "/
hmm", depending on how much they like you.
Homunculus you can only get them if you're an alchemist class (so "second job suffices" isn't enough - you *have* to be an alchemist or a creator. Likewise, to get the monster eggs (see above), you do not need to be an alchemist like the foreposter claims).
A homunculus will help you and kill monsters, and you get half of the experience they get. You can command them to do stuff (such as, go here, attack this, run away, but also more complex stuff if you know lua), and they can also do stuff on their own (they'll be protecting you!!) without you telling them. They have skills that differ from homunculus type to homunculus type, and you can either tell them when to cast them, or set them up so that they cast them on their own. They can level up, they have HP/SP, like you do, and they can die from monsters. In order to get one, you have to get an "Embryo" item. I sell them for 92k, you can get them from other alchemists, or create your own embryo using the "Pharmacy" skill (they can be quite costy if you don't have a lot of dex/luk though - in that case, buying may make more sense). Once you have an embryo, use the "Call Homunculus" skill (available if you level "Bioethics", which you get as alchemist from the special skill NPC) - it'll give you any of eight different homunculus. Two of them are Lif-type. If you get a different one and don't like it, you can delete it (Alt+R, Delete), and try again (you need another Embryo item). The homunculus you get is completely random. You can "desummon" a homunculus by casting "Rest" (homun's HP has to be >80%), and if you resummon it (or resurrect it), you will not need another embryo item. In fact, when you don't have your homunculus out, you don't have any item or anything (unlike pets with their "monster eggs") that show that you have a homunculus.
Lif are - IMO - weaker than Filirs, Vanils and Amistrs. To make up for that, they have Emergency Avoid which gives you a really high walking speed for a short time, so you can run away.
Do you have to be a certain level to own one?
Nope (Edit: to clarify, no minimum base-level requirement, but you need have enough job levels as alchemist to get the "Rest" and "Call Homunculus" skills)
In general, how do you capture monster eggs?
Monster eggs by taming (see above), Homunculus (which seems to be what you want) by casting "Call Homunculus" while having an embryo item on you.
Hope that helps
