。
She's incapable of telling a lie.
Literal
She [topic-は] lie [subject-の] cannot-tell person is.
The の after 嘘 marks the underlying object of つく ('to tell a lie') — but it's 嘘 that the potential つけない ('cannot tell') promotes to subject status, so what would be 嘘がつけない ('cannot tell lies') in a main clause becomes 嘘のつけない within the noun-modifying clause that describes 人. This が→の alternation is a productive feature of noun-modifying clauses in Japanese: 私の作ったケーキ is a common variant of 私が作ったケーキ ('the cake I made'). Older or more formal styles favor の; modern colloquial speech leans が. The whole sentence frames her as constitutionally honest rather than just truthful in any one moment.