If a woman fall inlove with a lesbian will that woman be also called a lesbian?

Depends on what kind of "love" it is, IMO.

If it's based in biology then that means one woman sees another woman as a means of procreation. Brains don't have absolute gender traits. Most to all brains have attributes that can be accorded to both sexes. There isn't really an absolute female brain and an absolute male brain.
People are naturally romantically attracted to others for mating purposes.
The brain switches trip to try and bond with another woman for mating purposes.
Same chemicals are released creating the pair bond.
If both women create that biological pair bond, then they both can be considered lesbians.

If it's based on social constructs and rationalizing then they are using different chemicals in the brain to induce a pseudo pair bond, mostly out of self image, identity.

One woman may be an actual lesbian and be able to pair bond with the other through the normal biological means, while the other couldn't "technically" be considered a lesbian since the same thing didn't occur in her brain.

For the other it would be more accurate to say she made a "life choice," or "image choice," even though she may not consciously realize it as such, she may truly believe she is a lesbian and that is what she's responding to. Wanting (due to an ingrained, basic, natural, atavistic need and desire, on some level) to be consistent in her identity.

Some people seem to think "love" based on identity isn't as "good" as "true" love, the natural pair bond.

People hate violence. The natural inclination of people is not violence or to kill. They have to be trained to put themselves into danger and kill. They have all sorts of problems the more it's against their identity (ptsd).

The military does this by taking away individual identity and making their identity that of a unit, a group.
Soldiers don't really go out to kill other people, they go out to protect the people in their unit, their group, their brothers and sisters. To protect their identity.
People had a huge fear of gay people. It threatened their identity.
So much that some offer violence. Killing, beating, bullying, humiliating, ostracizing gay people. Even though violence is abhorred.
It's protecting their identity.

People will kill to protect their love, people will kill to protect their identity.

The only real "problem" with identity based love is that it isn't self perpetuating or healing like biological love.
Biological love is more adaptable to change than identity based love.
When the identity changes too much, relationships based on it can't survive.
Ask any soldier that spent a significant amount of time in the military or in combat how difficult it is to transition to a "normal" life.

Love based on the biological process can change and grow.
Love based on identity will only last as long as that identity is protected.

That may have been off topic.
By this:

did you mean "if a woman that lived a 'straight' lifestyle falls in love with a lesbian and pursues a relationship with the lesbian, will that woman be called a lesbian by the members of her family and people she knows, society?"

Then probably.
Unless she's also banging dudes, or they have an open commune like relationship. Then she'll probably be called bi or freaky deaky or something by some people.

Ummmmm, yes.

She could also be called a dyke

Absolutely .. but there are also so called Marbles .. married but lesbian.

So that's how they roll.