Cersei and Jaime’s losses have to do with identity. Jaime’s is much stronger there, since his right hand is really the key to his identity as a warrior and a man and as Cersei’s mirror. Not only does he feel useless without it, its loss sends him into a crisis, a spiraling search for a new center and establishment of identity. (There’s much more on this in asoiafuniversity, I suggest a sidebar search for “Jaime identity”.)
Cersei’s hair, while it is part of her identity as a woman — as a beautiful woman — differs in that, well, hair grows back. Her pride is also not lost for good; though Kevan thought she was broken, I’m sure she’s going to come back from the humiliation of her Walk. And even if the people don’t respect her or think of her as the most beautiful woman in Westeros anymore, she’ll deal. Her true losses are her son and father, and her mirror/knight Jaime. And eventually, she’s going to lose her other children, and all her power as well.
Tyrion’s nose… well, there’s a situation where he was already considered ugly by his culture, but this injury made it far worse, undeniable. (GRRM has a habit of adding injury to insult, acually.) So it wasn’t much of a loss of anything, not even his illusions (he never liked mirrors even before). His true loss during the course of the series was that of (the illusion of?) his respect and power via his arrest and trial, the loss of his illusions about (and love for) Jaime through the Tysha reveal, and then the loss of his privilege and money through his exile and disguise.
And I’m sorry, when you include “Joffrey and Tywin lose their lives” in a question about the theme of loss for the Lannisters, I think you’re kind of reaching. It’s not exactly a loss that can affect them at all, because, well, they’re dead. The effects are on the living left behind, when Cersei, Jaime, and Tyrion lose their son/nephew and father. And for your last question, I’m pretty damn certain Tommen will lose his life as well, and Myrcella too I’m afraid.