How to describe the state of a locked door I have a question about the grammar behind saying what seems like a simple thing, but is proving to be hard for me. "The door is locked." In English it's an expression of state using an adjective.

However, research on  鎖 has not been very fruitful as it is apparently just a noun (actually it can act as a verb, my bad). The most consistent examples of "the door is locked" I have been able to understand from Jukuu have indicated this structure: 

門上了鎖。

First, is this correct? If so, what is the grammatical breakdown? I haven't run across a structure like this before, it doesn't fit a result complement or any other complement structure I know.

It seems like 上 is the verb. Is this the same sense as its use in 上廁所？  I'm also confused by the 了。Is it indicating change? Completion?
‘门上了锁’ is correct. 

I think you can best understand '上' here as 'put, set'.

Here there are 16 different definitions for 上：
8，11，13 and 14 approach the meaning here.

门上了锁 door set lock = the door has been locked = the door is locked

If there is a padlock on a door, it is also locked. (padlock is 挂锁）

'门上了锁。' could mean 'There is a padlock on the door.' or 'The door is locked.' or 'The door has been locked.' or even '(someone) put a padlock on the door.' depending on context.

'房门上锁是为了防盗。' was translated: 'The doors were padlocked to prevent theft.' 

都可以：

门锁了。The door is locked. / There is a padlock on the door.
门被锁了.
门上了锁。
门锁上了。
门（被）上锁了。   

*门（被）锁了上。 【不好】