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Lucky13 is a timing attack against the MAC in the CBC MAC-then-encrypt ciphersuites. In the attack's page:

The attacks involve detecting small differences in the time at which
TLS error messages appear on the network in response to
attacker-generated ciphertexts.

My question is: Can a passive adversary perform Lucky13? In other words, I need to know if Lucky13 attacker's model is active MitM or passive network attacker who just collect traffic and perform analysis afterwards?

The Lucky13 article on Our Results;

... attacks can be mounted by a standard man-in-the-middle (MITM) attacker who sees only ciphertext and can inject ciphertexts of his own composition into the network.

on the discussion;

We reiterate that the attacks are ciphertext-only, and so can be carried out by the standard MITM attacker, without a chosen-plaintext capability.

Can a passive adversary perform Lucky13?

No. The attacker must have the capability to inject chosen ciphertexts into the stream. A passive adversary (who listens into the encrypted traffic but cannot modify it) cannot do this.