>IAD Crossup
While it can be tempting to IAD j.B remember that while it does have a good hitbox, it doesn't make a very good crossup tool due to how far away from your opponent you would need to be to make it cross up and follow up off of, it is also very risky, since at that distance it can be anti aired pretty easily. Regular jump j.B is a much better cross up tool, it's actually pretty ambiguous, provided you do it at very close range.
>Knockdown
You're mainly looking to end your combos in a sweep so that you can set up 22A or 22B oki, (depending on the enemy distance.) However, you can't get sweep knockdown off of your better combos, so you usually just want to knock them down with 214A or J214B and just make them deal with wake up pressure (I dont know what much to do on basic wakeup with Labrys, I don't use her, I'm just pulling most of this data off the wiki)
>Punishing
Instant blocking is very important with this character, since none of her normals are faster than 7 frames. In general, all characters want to duck and look for overheads. All DPs and AoAs are unsafe on block, so you will want to look out for those to punish.
Labrys has a pretty decent anti air, that fatals in red axe, so if your opponent likes air dashing in, keep that in mind and make them think twice about approaching. Also if you fight a Narukami, feel free to use 2B whenever he raging lions, it's funny, and totally free.
>Safety
As a general rule, you only want to use j.B while falling, or during combos, also hold back while doing your falling j.Bs. The whole point is to make it safe. (There are always exceptions to the rules, keep that in mind.)
J214A is -13 on block, that is horrid. What you want to do if an enemy blocks your j.b and want to hit them with another overhead while still being safe is to use J.214AB that is only -3, and therefor unpunishable. (no attacking moves are less than 4 frames) but you will still lose your attacking momentum and have to start guarding. If you really want to mix it up, you could use J214a and then rapid cancel into a 2a, or just whatever pressure you'd like. The great thing about rapid canceling after your j214a is that if it hits (some people wont expect the double overhead) you can combo off it, when otherwise you couldn't.
Most moves are unsafe with Labrys, using 214A is -5 on block, so technically unsafe, but no character has a move fast enough that would hit far enough with the knockback it gives, so feel free to end pressure with that. If you have your opponent scared enough and can end pressure with 214B, that's even better, because that has a static difference of 0, which is great.
Also, always keep your finger on the grab tech button (if you're using a pad) or on C and D (if you're using a stick) you want to be able to actually tech a grab if you see it coming.
>Throw
Throws are mostly used as Labrys as an option during 22a oki, I don't usually see them in many other situations, so I can't help you there.
>Blockstrings
5AA, 2A>2A>2A>214A (each 2A is -1 on block, so the opponent cant really do anything, and you can react to dps in the middle, just don't mash too hard; use this as a baiting tool)
Labrys has VERY few good blockstrings, you just have to make due with what you have
>Furious Action
It is very bad. And i mean VERY bad, but it's not altogether useless. It can be charged, extending block time, and also super canceled (usually into 214214c/d (awaken only)) there are very few instances when this is useful, use with EXTREME caution, as it is very slow, and very unsafe. It will usually get you killed.
When starting out, try to record a lot of matches, and go over them at the end of the day to see where you went wrong, what you did right, and what you can improve on. In fact, this is a good habit to keep for players of any skill level.