In this work we extend the results of Amar et al. to a family of abstract functionals of autonomous type satisfying suitable locality and additivity properties, and general integral growth conditions of superlinear type. We single out a condition which is necessary and sufficient in order for a functional of this class to admit an integral representation, and sufficient to have an integral representation for its lower-semicontinuous envelope. We also show that the integrand $F(x,q)$ satisfies some nice regularity properties in the $q$-variable, in particular a convexity-type property along lines. By adapting the reparametrization techniques introduced in an earlier work by the author to the case at issue, we then prove that the family of integral functionals associated to integrands of this kind do meet the condition mentioned above; in particular, it is closed by $\varGamma$-convergence.