Breaking up a cat fight is dangerous for you. It's normal for cats to fight when they meet a stranger and since they're living in the same house they need to establish hierarchy. If the fights are overly aggressive (blood, screaming, etc.) you can separate Lucy into her own room again and start from scratch.
Generally, the best way to introduce cats is with patience. Leave the new cat in the room until the other cats stop growling/hissing so much (and leave the door alone). Letting the new cat roam the house and the old cats into the new cats room is a way to see what the old cats think and get them used to the scent. Getting three baby gates makes the next step easier as you can place all three in the doorway and reduce the possibility of fighting. Leave the door open when you're home (baby gates in place) and let them sniff and inspect each other.
Once the cats stop watching and hissing/growling at the new cat through the baby gates you can try letting the new cat out into the house supervised. Lots of high places, several litterboxes in good, open places, multiple food areas, etc. help the process along. Getting Feliway or Rescue remedy (I think that's what it's called) is great for relaxing tense kitties.
Aaaand... I think that's it...
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