Don't be in such a rush to duel Liz; by doing so, you'll make the encounter a lot more grueling, much like it will with other Rivals in REDACTED. She attacks you continuously, which makes it pretty annoying to dodge and counter without taking any damage. Here's some advice that may help you fight her at your best.
In order to get ready for the fight, start whittling her health with Damage Remote Attacks. To stop her from pulling any Remote Attacks on you, Stopping Remote Attacks gives you the advantage. Prioritize experiments in increasing your damage output from dashes and dashes attacks. Suits guiding you to the correct experiments are yours for the taking. Equip fast melee weapons.
Unlike most enemies, Liz won't be reeling from repeated hits during a fight and will be able to charge at you rather quickly. The best way to defeat her is to get really close to her and then run away from her before going back and causing damage. Then just rinse and repeat.
You'll really have the upper hand against her if you can wear experiments like High Tension Wire (Energy), which deals damage upon performing a dash attack. Another good experiment that you can try your hand at is Bombshell (Physical) in which you are able to run away dropping bombs that will land on her as she chases you around the room.
Since you can enter and exit her range pretty quickly without losing too much damage, the Barman Shankers are just about the perfect early-game melee weapon to use against her. You can buff up your Swing Speed and Melee Reach before fighting her, which will give you an advantage in the fight and let you get in a few stronger hits before she can react and dodge your assaults.
You'll have reached Sludge Tunnel by now, and physically you should be fit enough to duel Liz. The Sludge Suit will take 25% less damage on this level, so that definitely makes it an excellent choice. If you're more concerned with your experiments that you want to get for this fight, then the Physical Suit is the better option, followed by Energy Suit. With both of these, you increase your chances of finding powerful attacks that are performing well against Liz and make it find experiments in their respective categories more often.
No need to freak out if you didn't manage to kill Liz in your fight; what matters is you keep alive long enough to do continuous, far-range attacks on her. Once the lockdown timer reaches zero, she will try to escape, and you might not be in a position to kill her beforehand. For that reason, you should upgrade your Damage Remote Attacks ahead of your [REDACTED] run so you can make certain that at some point she will go down.