whta’s mean kept ?
Kept means to keep, in past tense.
What does “kept” mean?
As Dobie42 said, it is the past tense form of the verb “to keep.”
I kept, you kept, he/she kept, we kept, they kept.
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past of “keep”
Yes, kept is the past tense of keep, BUT the context is:
“Dr. Laura: Wait, help him and change him from what?
Katherine: From the lie that he KEPT, just help him get through it, basically.”
Even if one understands the expression “lie he kept”, it’s also harder to understand what on earth Katherine thought she could do to help her boyfriend in the circumstances. (In reality, she should have run for the hills! 
Not all native speakers would use the expression, “from the lie that he kept”. Neither do all say “kept a lie” (past tense) or “keep a lie” (present tense). I never do, myself. Instead, we can say he lied or was lying (by his actions or words, or both). We can also say “he lived a lie”.
In the podcast, Katherine said her boyfriend was substance-abusing (using drugs) behind her back (doing it secretly without her knowing) for a month. Her boyfriend acted as though he wasn’t using drugs during that time, but secretly he was. So he was lying to her by his actions. He “kept a lie”. He probably also verbally lied about it to her.
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