passing predicates to lowerBound, or alternatively, how lazy is map?

[Andrew Brown via Digitalmars-d-learn]

>
> You are correct. assumeSorted and lowerBound will provide 
> better time complexity than countUntil

I'm sorry, one final question because I think I'm close to 
understanding. Map produces a forward range (lazily) but not a 
random access range? Therefore, lowerBound will move along this 
range until the pred is not true? This means it would be better 
to do:

numbers.indexed(order).assumeSorted.lowerBound

than:

map(a => numbers[a])(order).assumeSorted.lowerBound

as the lowerBound will be faster on a random access range as 
produced by indexed?