In this paper we will study the isomorphism problem for the reduced twisted
group and groupoid Lp-operator algebras. For a locally compact group G and
a continuous 2-cocycle σ we will define the reduced σ-twisted
Lp-operator algebra Fλp​(G,σ). We will show that if pî€ =2,
then two such algebras are isometrically isomorphic if and only if the groups
are topologically isomorphic and the continuous 2-cocyles are cohomologous. For
a twist E over an \'etale groupoid G, we define the
reduced twisted groupoid Lp-operator algebra
Fλp​(G;E). In the main result of this paper, we
show that for pî€ =2 if the groupoids are topologically principal,
Hausdorff, \'etale and have a compact unit space, then two such algebras are
isometrically isomorphic if and only if the groupoids are isomorphic and the
twists are properly isomorphic