Shae reads like a character who exists as her own opposite—she's both Tyrion's love but also his prostitute on the payroll, the pleasure of his life but also his greatest burden. One moment, she can seem intelligent and worldly, and the next she can come across as entirely ignorant and naïve.
As a prostitute, Shae has developed the ability to read everything about a man at a glance. When Varys appears in one of his masterful disguises, she instantly spots him. Tyrion is pretty impressed, but Shae shrugs it off, saying, "A whore learns to see the man, not his garb, or she turns up dead in an alley" (45.Tyrion.52). Clearly, this is a girl who knows what is right for her and knows how to spot it, having developed certain skills to keep alive in the dangerous world of prostitution.
But other times, she is entirely ignorant of the world and people beyond her self-interest. When Tyrion decides it is time she moved from the manse, Shae suggests they move in together. Tempting Tyrion, she argues:
"Though I would be your lady, m'lord. I'd dress in all the beautiful things you gave me, in satin and samite and cloth-of-gold, and I'd wear your jewels and hold your hand and sit by you at feasts. I could give you sons, I know I could… and I vow I'd never shame you." (45.Tyrion.67)
Sounds great, but then Tyrion explains that Cersei will use Shae against him and likely harm her. Shae's answer is simply to kill her, which may be the most unrealistic response ever.
Another example of this is when Shae complains about Lady Lollys to Tyrion. As her chamber maid, Shae complains, "[Lollys] sleeps and she eats. Sometimes she falls asleep while she's eating. The food falls under the blankets and she rolls in it, and I have to clean her" (55.Tyrion.102). The fact that Lady Lollys had just been raped and became pregnant as a result completely escapes Shae—all she cares about is that Lollys is making her life more difficult, showing a lack of empathy for other people.
Shae's world clearly centers on Shae. Her natural tendency is to do what she needs to survive and survive as nicely as possible. With that said, though, her life likely warrants this worldview. The odds aren't exactly in her favor.
Tyrion is pretty wish-washy when it comes to Shae. On the one hand, he believes that "it is only the gold and jewels the whore loves" (45.Tyrion.101), but on the other, he thinks to himself "[Tysha has] haunted me half my life, but I don't need her anymore, […] I have Shae now. Shae" (30.Tyrion.88). By the end, though, it's pretty obvious he's more than smitten with her.
But the question of whether Shae loves Tyrion is left open by the novel's end. Shae proclaims her love for Tyrion, like asking to be his lady in the quote above. But she may just be really good at pretending, another survival trick she's picked up working as a prostitute. We'll have to wait and see how this love song plays out.