In general, if there is no extra work needed for the lazy variable after the initialization for it, it would be enough do declare it without the closure initialization.
For instance, for a simple string it is fair to implement:
lazy var myString = "a string"
However, when it comes to something needs more editing (setup) -like CLLocationManager
for instance-, you would naturally go with the closure initialization:
lazy var locationManager: CLLocationManager = {
var lm = CLLocationManager()
// here is one extra thing to do:
lm.delegate = self
return lm
}()
As mentioned, at some point we needed to do additional step(s) after the initialization (which is lm.delegate = self
in the above example).
Referring to your case, since there is nothing should happen after the initialization, both:
lazy var test1: String = String("a string")
and
lazy var test2: String = { String("a string") }()
are the same. You should go with the first one as a shorthand typing.