The worst thing to do is try to force anything. The reason Lucy fled when
you put her in Natasha's room is because he took her from her territory
and put her in Natasha's. They are deeply territorial. Two thoughts: first,
if Natasha
hid for months before you got Lucy, this might just be the way she is--very
timid and not very socialized. She may be this way with other cats and
people. What is her history? Is she a shelter/pound cat, acquired as an
adult,
or raised by you from kittenhood? Second: patience will do the trick. It
sounds
like you have enough space for them to each have their own territory. This
means that Natasha needs to have not just a bed to hide under but
nice places to be upstairs, such as a window cat shelf or cat tree, and her
own box. Same with Lucy downstairs. In time, they will adjust to one
another.
This worked with my girls, and has worked with others. (Mine don't sleep
together but have begun to play and hang out in the same rooms after three
years. It tool them about eight months to stop posturing and get curious
about one another.

I would sure switch them back and forth. Then begin trying a lot smaller
introduction periods separating immediately when you see aggression. It may
take a very long time, but they should be able to co exist. I got a cat that
now at 2 years really does well. But the key was equal time out and
extending the periods of time they are together. Then as they did better,
but just got mouthy at each other, I kept closed tubs of food around and
anytime agression happened I would grab a handy tub and distract them with
food (yummy treat. For mine it happened to be Meow mix - not what I normally
feed them.) Megan gave me that advice and it is probably the best way of
getting them out of that loop I have seen. It has taken a long time, but
they do well now.