The US Census Bureau defines lower class as the lowest 20% of incomes.
Pew defines it as the lowest 2/3 of the median.
If the highest income is $100, 20% is $20.
At 2/3 the median, if the median is $30, lower-class is $20.
Is there a reason they’re tying income classes to people within those classes, and not what it costs to survive within the economy?
For one thing, it maximizes the amount of information the census contains: if you’re splitting a group into bins, the splitting with the lowest entropy is the one with equal-sized bins. If the bin sizes fluctuate with time (as a proportion of the overall population), the amount of information the census captures will vary as well. If your definition of lower-income includes 100% (or 0%) of the population, then assigning someone to a category tells you nothing about them you didn’t already know.