To know someone = be familiar or friendly with someone To meet someone [for the first time] = see or be introduced to for the first time
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New2grammarYou've been lying to me since the first day I [know/met] you.I would suggest that "since the first day" indicates "met" rather than "know".
New2grammarYou've been lying to me since the first day I [know/met] you.As a footnote: it might be more natural to say: