Hi,

debian/control has:

  liblightdm-gobject-dev (>= 1.4.0) | liblightdm-gobject-1-dev (>= 1.4.0),
  lightdm-vala | liblightdm-gobject-1-dev,

The alternatives were added upstream in 2015 ("Make arctica-greeter build
on Debian and Ubuntu alike") because Ubuntu's lightdm then shipped
liblightdm-gobject-1-dev, including the vapi. That's no longer the case:
since plucky, Ubuntu ships liblightdm-gobject-dev and lightdm-vala like
Debian, with a transitional "Provides: liblightdm-gobject-1-dev".

Because of that Provides, the "lightdm-vala | liblightdm-gobject-1-dev"
alternative is satisfied without lightdm-vala, so the vapi is missing and
the build fails in Ubuntu:

  error: Package `liblightdm-gobject-1' not found in specified Vala API
  directories or GObject-Introspection GIR directories

https://bugs.launchpad.net/bugs/2120577

liblightdm-gobject-1-dev doesn't exist in Debian, so dropping the
alternatives (attached patch) doesn't change anything there and would let
Ubuntu sync the package again.

Thanks,
Sebastien Bacher