After reviewing the definitions and some properties of the Lah numbers and the Stirling numbers of both kinds, as well as their generalizations (r-Lah numbers, r- Stirling numbers of both kinds and (l, r)-Stirling numbers of both kinds), we define the (l, r)-Lah numbers analogously, prove a recurrence relation that they satisfy, express them explicitly as a multiple sum, and present the difference-differential equations satisfied by their column and row generating functions, respectively. Finally, we pose two conjectures, based on experimental evidence.