In distributed storage systems, codes with lower repair locality are much more desirable due to their superiority in reducing the disk I/O complexity of each repair process. Motivated partially by both codes with information (r,δ1)c locality and codes with cooperative (r,l) locality, we propose the concept of codes with information (r,l,δ) locality in this paper. For a linear code C with information (r,l,δ) locality, values at arbitrary l information coordinates of an information set I can be recovered by connecting any of δ existing pairwise disjoint local repair sets with size no more than r, where a local repair set of l coordinates is defined as the set of some other coordinates by which one can recover the values at these l coordinates. We derive a lower bound on the codeword length n for [n,k,d] linear codes with information (r,l,δ) locality. Furthermore, we indicate its tightness for some special cases. Particularly, some existing results can be deduced from our bound by restriction on parameters.