This is a good question.
Lucia works for a lawyer who depends on her for everything. For example, answering the phones. 
The second half is not a sentence.
Lucia works for a lawyer who depends on her for everything: for example, answering the phones. 
This works but is a little unusual.
Lucia works for a lawyer who depends on her for everything. That is, she answers the phones. Too messy.
Firstly, let's tackle the "who depends on her..."
If this is just additional information about the lawyer, then it should read:
Lucia works for a lawyer, who depends on her for everything.
If it is required to identify the lawyer then your version is correct.
It is more obvious if you substitute in 'who lives upstairs'.
She works for the lawyer who lives upstairs. (identifies him)
She works for the lawyer, who lives upstairs.
(just tells you something about him)
Let's look at the original question:
Lucia works for a lawyer who depends on her for everything; for example, answering the phones. this is standard convention
Lucia works for a lawyer who depends on her for everything (for example, answering the phones). this is also standard convention but many like to avoid brackets in official correspondence.
