TL;DR - functional programming taught me that LSP is a special case of PLS: Principle of Least Surprise.
One thing that bugs me while reading Java: I'm reading along, come to a method call, ctrl-click on the method name, and get a list of implementations of the interface. IntelliJ can't tell me exactly what will run at this point in the code. Java has dynamic dispatch: it decides at runtime which implementation to run.
Functional style has a different concept to offer instead of Java's interface. It's called "typeclass," which is incredibly confusing. Please accept that this idea has little to do with "type" or "class."
While an interface says, "This class can perform this method," a typeclass says, "There exists something that can perform this method on this class." (using 'class' loosely) An interface is baked into a class, while a typeclass instance is provided separately.
With typeclasses, the method implementation isn't attached to the runtime class. Instead, the compiler digs up the typeclass instance, based on a declared type instead of a concrete runtime type. This isn't flexible in the same way as OO's dynamic dispatch, but it has the advantage that we can tell by looking at the code exactly which implementation of the method will execute.
This gives us better ability to read the code and figure out what will happen in all circumstances, without using the debugger. Functional programmers call this "reasoning about code."
In Java, how can we make statements about what the code will do when we don't know exactly what code will run? One answer is: Liskov Substitution Principle. This OO design principle says, If you inherit from some other class or implement an interface, then be sure your class meets all expectations people have of the superclass or interface. The compiler enforces that our methods have the right signatures, while LSP demands that our implementation have the same invariants, postconditions, and other properties implied the documentation of the superclass or interface.
For instance, if you create an implementation of List with a .length() method that sometimes returns -1, you violate the expectations people have for Lists. This surprises people. Surprises are bad. Surprises stop us from accurately predicting how code will execute.
Therefore, the Liskov Substition Principle says, "Don't surprise people." If the documentation of List implies that length() will return a nonnegative integer, always do that. Also make sure that your List is 0-indexed like everyone else's. To implement an interface is to take on all the implicit and explicit promises made by that interface. That's LSP.
In Haskell or Scala, we can use typeclasses and be certain what the code will do at runtime. In Java, we can have the flexibility of dynamic dispatch and still have some knowledge of what will happen at runtime as long as we respect the Liskov Substitution Principle.