Yes, Clark Kent explicitly learns that Lex Luthor was responsible for the murder of his father, Lionel Luthor.
The Revelation of Lex's Crime
Clark's understanding of Lionel's death takes a definitive turn through a crucial conversation and a vital discovery. His journey to uncover the truth begins when he shares a message from Lionel with Chloe Sullivan at the Isis Foundation. Lionel's message hinted at a profound secret, emphasizing its connection to a set of specific keys.
A Key to Understanding the Motive
During their conversation, Chloe reveals a critical piece of information that brings clarity to Clark's suspicions. She discloses that Lionel had deliberately left one of these significant keys for Clark, storing it in her desk for safekeeping. However, the key was no longer there; Lex Luthor had already taken it.
This revelation serves as the pivotal moment for Clark. Connecting Lex's acquisition of the key directly with Lionel's cryptic message and his subsequent death, Clark immediately deduces the grim truth: Lex killed Lionel precisely to obtain this vital key. This establishes Lex's motive beyond doubt.
Overwhelmed by this shocking and concrete realization, Clark wastes no time. He promptly super-speeds off, presumably to confront Lex or act on this newfound, devastating knowledge.