No joke: Lena (Llewelyn) Gu is a therapist who might need some therapy. We diagnose her as Robert Gu-phobic. Lena is Robert's ex-wife who dislikes him so much that she faked her own death (sort of) when he got his Alzheimer's cured. Really, Lena is useful to us readers because of her relationship to Robert, which is less love-hate and more hate-hate, with an extra side of hate.
But let's get some boring facts out of the way. (Note: we may be wrong and some of these facts might spark an excellent paper topic for you.) Lena is from Britain originally (8.7) and she's a therapist who—as big-jerk Robert notes—was "rather well known in a limited, humdrum way" (3.62).
Wow, the fact that Robert says that makes it less surprising that Lena faked her own death (with help from the Friends of Privacy). Now, let's be clear, old Lena isn't all sunshine and lollipops. Like Robert, she's old and has to be prodded into trying out new computer technology. (Guess who does the prodding? Miri, because she prods everyone into action.) She doesn't get the physical rejuvenation that works for Robert, so Lena is confined to a pretty sweet wheelchair.
But what's most confining to Lena is probably her hatred of Robert. Lena may be pretty perceptive when it comes to other people, as Xiu Xiang comes to learn (34.79): Lena gives a good summary of Miri's personality (34.83); and she's behind Xiu Xiang's correct diagnosis of Tommie Parker's issue (34.44-6). Then, when it comes to Robert, she's always ready to give the worst interpretation of his motivations. She switches between calling him "You-Know-Who" and "the monster" (13.59, 96).
And even when we know that Robert has slowly shifted, Lena keeps thinking mean thoughts about him: for instance, when Robert tries to distract Juan (who is sad that Miri isn't being friendly), Lena says,
"Can you believe this jerk? All he wants is to trick some more help out of the boy." (33.65)
We know this isn't true because we just read the scene from Robert's POV. When Juan teaches Robert how to play synch-monster and Robert says that they could do better, Lena says,
"See? He's always complaining. Give him another minute and he'll be making sly claims that you are to blame for everything that went wrong." (14.34)
There are several of these moments when Lena sees something and tells us that Robert is a monster… because she's seriously biased. For all Lena's perceptiveness with people, she can't see that Robert's growing as a person. Paradoxically, having her remind us what a jerk he was actually shows us how much he's grown.