What is meant by the notation $L(...)$?
This link confirms my intuition that $L(R)$ where $R$ is a regular expressions simply means "the language produced by the regular expression $R$".

In that case, $ab \in L_2$ but $ab \notin L_1$

In case link is down:

Operators used in regular expressions include:

Union: If R1 and R2 are regular expressions, then R1 | R2 (also written as R1 U R2 or R1 + R2) is also a regular expression.
L(R1|R2) = L(R1) U L(R2).

Concatenation: If R1 and R2 are regular expressions, then R1R2 (also written as R1.R2) is also a regular expression.
L(R1R2) = L(R1) concatenated with L(R2).

Kleene closure: If R1 is a regular expression, then R1* (the Kleene closure of R1) is also a regular expression.
L(R1*) = epsilon U L(R1) U L(R1R1) U L(R1R1R1) U ...