Summary: Both the complete and incomplete Bell polynomials are multivariate forms for Bell polynomials and Stirling numbers of the second kind. These polynomials are a crucial role in enumerative combinatorics. Recently, H. K. Kim introduced both the central Lah numbers and \(r\)-central Lah numbers. With this in mind, this paper will be subdivided into two parts to address the above mathematics concepts: in the first part, that will be a question of introducing both complete and incomplete central Lah-Bell polynomials, as multivariate forms of the central Lah numbers and the central Lah-Bell polynomials, respectively. We give a relation between the central Lah-Bell numbers and the complete Bell polynomials by using the Kölbig-Coeffey equation. This entail deriving explicit formulas for these polynomials and numbers, as well as conducting research into some identities for these polynomials. In the second part, both the \(r\)-central complete and incomplete Lah-Bell polynomials as multivariate forms of both the \(r\)-central Lah-numbers and the \(r\)-extended Lah-Bell polynomials are introduced and also are derive explicit formulas and several noble identities.