<p>The multicritical generalizations of the Lee-Yang universality class arise as renormalization-group fixed points of scalar field theories with complex <i>iφ</i>^2<i>n</i>+1 interaction, <i>n</i> ∈ ℕ, just below their upper critical dimension. It has been recently conjectured that their continuation to two dimensions corresponds to the non-unitary conformal minimal models ℳ(2<i>,</i> 2<i>n</i> + 3). Motivated by that, we revisit the functional renormalization group approach to complex 𝒫𝒯-symmetric scalar field theories in the Local Potential Approximation, without or with wavefunction renormalization (LPA and LPA’ respectively), aiming to explore the fate of the <i>iφ</i>^2<i>n</i>+1 theories from their upper critical dimension to two dimensions. The <i>iφ</i>^2<i>n</i>+1 fixed points are identified using a perturbative expansion of the functional fixed-point equation near their upper critical dimensions, and they are followed to lower dimensions by numerical integration of the full equation. A peculiar feature of the complex 𝒫𝒯-symmetric potentials is that the fixed points are characterized by real but negative anomalous dimensions <i>η</i>, and in low dimension <i>d</i>, this can lead to a change of sign of the scaling dimensions ∆ = (<i>d</i> − 2 + <i>η</i>)<i>/</i>2, thus requiring a novel analysis of the analytical properties of the functional fixed-point equations. We are able to follow the Lee-Yang universality class (<i>n</i> = 1) down to two dimensions, and numerically determine the scaling dimension of the fundamental field as a function of <i>d</i>. On the other hand, within the LPA’, multicritical Lee-Yang fixed points with <i>n &gt;</i> 1 cannot be continued to <i>d</i> = 2 due to the existence of unexpected non-perturbative fixed points that annihilate with the <i>iφ</i>^2<i>n</i>+1 fixed points.</p>