Given a reduced plumbing tree and a spin-c structure, I will discuss how to construct a plumbed 3-manifold invariant in the form of a Laurent series twisted by a root lattice. Such a series is invariant under the Neumann moves on plumbing trees and the action of the Weyl group. These series-valued invariants generalize the Z-hat series of Gukov-Pei-Putrov-Vafa, Gukov-Manolescu, Park and Ri. They are motivated by the study of the WRT invariants, and the work of Akhmechet-Johnson-Krushkal which found connections with lattice cohomology. Time permitting, I will also discuss a multivariable generalization of the root lattice-twisted series for knot complements and gluing formulas. This is joint work with N. Tarasca.