What are the current meta picks for each lane?

Whatever you're good with is good enough in the meta.

It's 5.6, baby.

Depends on what you're asking. The meta typically refers to the general team comp and lane pick, but not necessarily the champion.

The laning meta, for example, has been 1-1-2-1 (One top, One mid, Two bot, One jungle) for quite some time. In high levels of play you might see it 2-1-1 instead with one side lane-swapping top and bot, but for most games the first is the standard.

Then there is the overall Champion Meta, such as the newly rising "Tank Meta". This generally refers to nerfs or buffs to the overall game that favors one class of Champion, making them seem unusually strong in comparison. Recently, they've given Tanks more options in the jungle (by making Cinderhulk a strong and useful item pick) among other changes. This makes Tank champions more common, especially in the jungle. In turn this can effect the champ picks in lane. Top or Support can typically be more damage-focused or mage-focused, respectively, because they already have a Tank pick in the team comp.

If you're asking about what specific Champions are "meta" in a specific lane - that depends wildly on what tier of play and if its Draft or not. Some Champions may have recently gotten buffed and so become popular and seemingly dominant in most games. These are referred to as "Flavor Of The Month" because (usually) they will eventually either get nerfed or the player base will start to change their strategies.

However in terms of pro players, they will often know specific player strengths. One player, for example, may be an epic Vayne player, so they will nerf that Champion even if Vayne isn't specifically a strong pick in general terms.

Does it matter?

If your champion can do fine in a certain match-up (in draft) or can do relatively fine against most champions in its lane, fits the team comp and contributes something the team needs (no frontline + not a lot of cc means Fiora probably is not the best pick up top), and you can play them well, then what does it matter?

Don't pick meta champions because they're meta, pick them because you understand why they're meta or choose something you're good at.

Just about everything can be considered meta. Once Urgot was proven to be a decent pick, everything came in to party.