Programming languages are expected to support programmer's effort to structure program code. The ML module system, object systems and mixins are good examples of language constructs promoting modular programming. Among the three, mixins can be thought of as a generalization of the two others in the sense that mixins can incorporate features of ML modules and objects with a set of primitive operators with clean semantics. Much work has been devoted to build mixin-based module systems for practical programming languages. In respect of the operational semantics, previous work notably investigated mixin calculi in call-by-name and call-by-value evaluation settings. In this paper we examine a mixin calculus in a call-by-need, or lazy, evaluation setting. We demonstrate how lazy mixins can be interesting in practice with a series of examples, and formalize the operational semantics by adapting Ancona and Zucca's concise formalization of call-by-name mixins. We then extend the semantics with constraints to control the evaluation order of components of mixins in several ways. The main motivation for considering the constraints is to produce side effects in a more explicit order than in a purely lazy, demand-driven setting. We explore the design space of possibly interesting constraints and consider two examples in detail.