Learn Dutch: Lotions gebruikt hij er liever drie verschillende. - Lotions, he prefers to use three different ones.

The full object of the sentence is drie verschillende lotions (three different lotions). In this structure, the noun lotions is moved to the very front to establish the topic, while the quantity and adjective (drie verschillende) are left behind later in the sentence.

What is the exact function of er here?

This is the quantitative er. When you state a quantity like drie (three) but the noun it refers to (lotions) has been moved away or omitted, Dutch requires er to act as a placeholder. It translates roughly to "of them".

Why is the word order gebruikt hij instead of hij gebruikt?

Because the sentence starts with the fronted object Lotions, it triggers the verb-second (V2) rule. The verb gebruikt must take the second position in the main clause, which forces the subject hij to invert and move right after it.

Why does the sentence use liever instead of a specific verb meaning "to prefer"?

While Dutch has verbs like verkiezen for "to prefer", it is much more natural and common to express preference by adding liever (the comparative of graag) to the main action. So "he prefers to use" becomes gebruikt hij liever (literally "he uses rather").