Why does Luv cry?

Question

I watched Blade Runner 2049 twice already and I think I have almost everything figured out. The one thing though that I still can't understand are these moments where Luv cries:

• In the scene where Wallace examines the new replicant model (BTW what does he mean by "new model"?) Luv sheds a tear when he approaches the Replicant (even before he kills her). Is it because she knows what Wallace will do, and she sympathizes?
• She also sheds a tear while killing lieutenant Joshi. Is it because she doesn't really want to do it?

In the final waterfront fight Luv also angrily kisses K.

What is happening? Why does she do all these random (and very human) things?

Answer 1

She is in awe of Wallace and she doesn't want to disappoint him

Luv is living in awe of Wallace, she looks up to him and even thinks that he has named her:

Luv holds back. Knows better than to help without asked as he begins his examination.
NIANDER WALLACE (cont’d)
Bring the one for micronics, would you,
luv. Ah, “luv.” A diminutive. Not a name at all, though taken
for one. Luv brings a small wooden box. ...
The electrodes fit into wetware receivers within and... the
device glows to match the new light in the Barracudas’ eyes,
enabled.
Luv’s hands shake as she closes the box. Beyond respect, she
lives in perpetual awe of him.
_{-Final Shooting Script, Blade Runner 2049 (2017), Green, M., Fancher, H.}

Once Wallace is done with his speech about wanting to take over the universe, he tasks her with bringing the last piece of the puzzle:

THE MODEL COLLAPSES.
NIANDER WALLACE (cont’d)
His last trick. Procreation.
Perfected... then lost. There is a
child. Finally unearthed. Bring it to
me. Bring it to me. Bring it to me.
ON LUV: An eye waters at the thought of disappointing him.
LUV
Sir.
He reaches behind his head, removes the HALO. Preferring the
darkness.
NIANDER WALLACE
The best Angel of all. Aren’t you, luv?
ON LUV: Her jaw sets. She will not disappoint Mr. Wallace
_-Ibid.

So you see, Luv is in perpetual awe of Niander and even petrified at the thought of disappointing him.

Answer 2

I think that Luv had originally a very "human" personality, but that spending time working and living so close to the monster that is Wallace, made her lose this part of her personality.
If think she did not have the choice, because she is effectively a slave to Wallace (he could surely have her destroyed whenever he feels like it ; remember the air-to-surface weapons Luv has access to, Wallace certainly has access to worse). The only way for her to survive is to hide her feelings from him and act as the machine Wallace wants.
Now from time to time she will allow herself to let a human feeling exude - or maybe she cannot always hide all of them.

By the way the new model Wallace is referring to is a type of replicant that can reproduce, give birth to babies. Wallace is interested in controlling more and more replicants and think he can by controlling their reproduction.