Actually no. Lizze McGuire couldnt hold a candle to Hannah Montana in terms of popularity. Im actually surprised they took this long to make fun of Miley though (as one could say this is def the tail end of her Hannah Montana days).
As in the matter of aging...I don't really see how wether an episode ages poorly or not matters in the least bit. A lot of the episodes from the Golden Age of the Simpsons have aged horrible (especially the ones from the first three seasons) as one would have to of been a teenager in the late 80s early 90s to fully understand a lot of the lines, titles, gags, and plots. If someone 5 years down the line looks at the title Hannah Banana and goes "i dont get it" it would be no different then a 12 year old in 1998 looking at the episode title Lisa the Greek (a play off Jimmy the Greek, a famous and popular bookie who was good at predicting who would win) and saying the same thing. Point is it doesnt make the episode any less enjoyable, spectacular, what have you.