What's the difference between phi and lambda in regular expression?
You need to distinguish between regular expression syntax and its interpretation aka semantics.


"$\lambda$" is a symbol representing the set that contains only the empty string $\{\varepsilon\}$).
"$\phi$"¹ is a symbol representing the empty set of strings $\emptyset = \{\}$.


The difference becomes apparent when you compute the interpretation $i$ of a regular expression:


$i(a\lambda) = i(a) \cdot i(\lambda) = \{ a \} \cdot \{ \varepsilon \} = \{a\}$

Note: I'm deliberately using $\varepsilon$ to denote the "real" empty string outside of a regular expression. Your source probably uses $\lambda$ for both; that obscures the fact that it's used in two different ways.
$i(a\phi) = i(a) \cdot i(\phi) = \{a\} \cdot \emptyset = \emptyset$.


If you don't follow that last line, revisit the definition of the concatenation of languages:

$\qquad\displaystyle A \cdot B = \{ a \cdot b \mid a \in A, b \in B\}$.




Do they really use $\phi$?