Meromorphicity of the $(2,2)$ theta lift for non-isotropic lattices

Let $L$ be a signature $(2,2)$ lattice with no isotropic vectors, let $K_{\mathbb{R}}+iC\cong\mathcal{H}\times\mathcal{H}$ be the associated domain, and let $\frac{i^{m}}{2}\Phi_{L,m,m,0}$ be the weight $m$ automorphic form. Let $R_{m}^{(2)}$ be the weight-raising operator.

Non-isotropic $(2,2)$ meromorphicity conjecture. The image of $\frac{i^{m}}{2}\Phi_{L,m,m,0}$ under $\frac{1}{-4\pi^{2}}R_{m}^{(2)}$, namely $\frac{\delta_{m,\tau}\delta_{m,\sigma}}{-2\pi^{2}}$, is meromorphic, with the singularities given in Theorem Rmb-2Phimer, also when $L$ contains no isotropic vectors.

The result for $b_{-}=1$ is independent of isotropic vectors, while the Fourier-expansion argument used for general $b_{-}$ requires them. Meyer's theorem leaves precisely this $b_{-}=2$ non-isotropic case as the unresolved case addressed by the conjecture.