I tend to subscribe to the philosophy that language designers should be as strict as possible; choose the "best" syntax for doing something and only allow that unless there's really compelling reasons for alternatives.
cats.map{|c| c.name} |> print
print(cats.map{|c| c.name})
If you're grabbing the constructor as a function, for example, then it's a bit more sensible to use Cat instead of Cat.new. I don't know...it seemed at the time neat to allow a shorthand way of constructing something, but it's kinda wonky.
This is refreshing from other newish (cough golang) languages which pick the "wonky" path, but go on to defend it tirelessly. Keep up the good work.
On the other hand, Lily is a type-safe language with generics. The kinds of "metaprogramming" that you would try to do with Python classes-as-objects might be done in different ways in Lily.
More theoretically, the whole point of types (as sets) was to was to be a qualitively distinct layer of things that could not be mixed up in logically paradoxical combinations with other objects. That abstruse point of logic might or might not have practical implications for a real-world programming language.
My immediate reaction to the name "Lily" is positive, evokes a sense of calmness, and suggests an elegant, well-structured set of tools.
Regarding constructor syntax, probably "Cat.new()" is more common or conventional. I kind of like "Cat()" as it's less verbose, noisy. However I see what you mean about allowing classes as values, if not entirely clear to me how that feature would absolutely demand one syntax over the other.
I agree with other comments, Lily is an outstanding one-person effort! That its creator is self-taught only adds to its charm.
The piping is more an example of how piping works with everything and that, yes, the new method really really is a method instead of some magical keyword.
But I stand by piping: https://lorgonblog.wordpress.com/2008/03/30/pipelining-in-f/
So is the .new() method in that case an alternate constructor (i.e. constructor code will not run only the contents of the new method will) or is it a method being invoked after the constructor code runs?