  In this paper we consider a super-renormalizable theory of massless QED in
$(2+1)$ dimensions and discuss their BRST symmetry transformation. By extending
the BRST transformation we derive the Nielsen identities for the theory.
Further, we compute the generalized BRST (so-called FFBRST) transformation by
making the transformation parameter field-dependent. Remarkably, we observe
that the Lowenstein-Zimmerman mass terms, containing Lowenstein-Zimmerman
parameter which plays an important role in the BPHZL renormalization program,
along with the external sources coupled to the non-linear BRST variations
appear naturally in the theory through a FFBRST transformation.
