I believe that SEL implements its themes of progression by showing the contrasts between Eastern and Western cultures (broadly speaking). The progress of society is shown, therefore, not only through technological innovations but also through globalization and the effects it has on the disparities between the actions of older generations and the newer ones. Note that I will make wide generalizations in this analysis.
So, getting to it, I will be comparing the parents in Lain's family with their children. The parents are seen to be a traditional family, with the male being responsible for the money-making and the female for the well-being of the household. From what we see of them, they are loyal to one another and fulfill their general duties towards their children. These I would label as parts of Eastern culture.
When we get to Lain's sister, however, we can see that she at one point leaves the dinner table, excusing herself by saying she's had enough, no doubt a subtle sign of her Anorexia. This mental illness being a chiefly Western one and her leaving the dinner table prematurely being chiefly Un-Eastern or Un-Japanese as well as her having casual, undevoted sex in one of the later episodes depicts her distance from her family, culturally speaking.
Lain also falls in the more Western side of things since, as one can see, she only eats with a Western-style spoon while all the rest of her family use chopsticks. She also visits clubs and is implied to date individuals in a promiscius manner, at least in one of her personalities.
It's showing how people change as they get more connected to one another and identities and cultures mend together to the point that people are unable to retain their own identities and culture, ultimately becoming blank slates as evinced by the conclusion to the arc of Lain's sister.
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