Currently I have been having a hard time carrying games as assassins(Zed,Lissandra,Kassadin) because I just can't get past the tank line to kill the back line so I usually just end up dying trying to force my way through them. Any champions I should learn that can deal consistent damage so I can kill the tanks. Also if you have any tips on how to play assassins in this tank meta I would really appreciate it.
In my expirience:
Cassio, Karthus, Vlad are all good at taking down tanks
Honorable mention to Viktor who is quite good against them once he has both Q and E fully leveled and 4 items (lichbane cdr rab and void) but he takes a while to get there so he's not as reliable as the others
Malzahar can do it well enough. Mordekaiser can do it very well with his ult and anivia can do it to some degree. Malz and anivia can easily become very assassin like which seems to be your preferred champ style.
come at me
basically, look for: 1.) high sustained damage 2.) survivability, mobility and/or range 3.) ability to build Liandry's effectively. If a champ has 2/3, it is good against tanks.
Lissandra is a mage not assasin
Will seriously melt tanks like theyr'e nothing.
You should learn to play Mage which give sustain dmg, like 
. It is very hard to play Assassin right now. When you have only one target (often ADCs while most of mid-laner will have a Zhonya as a 2nd item), the counter is extremely hard. Just one or more hard CC, or ADCs get an early banshee, you will be rekt all the time.
