PSA : Vs New Rift Herald In Lane
The towers prioritize minions over Rift Herald, so clear the minion wave 1st before you focus on her so the tower will focus onto her as well.
Her damage hard scales with her current HP, this means the more damage you do to her the weaker she is. A strategy you can use vs a team that took her eye (the item used to summon her) is to keep the wave pushed toward their tower the best you can before she's summoned. There is a time limit in which she can be summoned so if you can stall long enough with your minions pushed up to the enemy tower she will have to travel the entire length of the lane first to reach your tower, giving you time to damage her some to drop her damage vs your tower when she inevitably reaches it.
This part is the same concept as the 1st point I made about towers, but if she's near your tower's range with enemy minions you should destroy the minion wave 1st so she won't have anything else drawing tower aggro from her when she charges it.
These are just some tips to help people that don't completely understand or know how her lane presence works. Have a nice day.