Well dynamic is dynamic, scala is for designing DSL with good static properties.
Dynamicity means you are responsible for error dispatching.
There are a lot of approaches applicable, but parsing lambdas means designing a new language.
So you probably need to read about functional language design.
Then you can formulate your langauge expressions in form of some recursive ADT or GADT and develop nice interpreter.
Scala can help you with parsing llibraries and data processing, but generally you are on your own here