The trend of applying LASSO regression to compositional data is expanding, making it valuable across scientific domains. Lasso regression methods utilise a penalty function expressed as a norm within the space of model coefficients, determining the relevance of coefficients in the model. For models incorporating compositional covariates, the norm should align with Aitchison’s geometry. This paper contributes by exploring the \(L^1\) -norm for the penalty term of LASSO regression in a compositional context. This involves introducing a rigorous definition of the compositional \(L^1\) -norm, considering the unique geometric structure of the compositional sample space. A real dataset on physical activity is used to show how our proposed method facilitates the differentiation between balances that influence the response variable and those that are inconsequential.