Abstract A standard approach for inference in probabilistic formalisms with first-order constructs is lifted variable elimination (LVE) for single queries. To handle multiple queries efficiently, the lifted junction tree algorithm (LJT) employs a first-order cluster representation of a model and LVE as a subroutine. Both algorithms answer conjunctive queries of propositional random variables, shattering the model on the query, which causes unnecessary groundings for conjunctive queries of interchangeable variables. This paper presents parameterised queries as a means to avoid groundings, applying the lifting idea to queries. Parameterised queries enable LVE and LJT to compute answers faster, while compactly representing queries and answers.