The lift at my work for example, groundfloor is '1' and the next floor up is '2' and so on.
Whereas other lifts, ground floor is 'G' and the next floor up is '1'.
Is there a reason for this inconsistency?
Yes, different countries have different definitions for that floor.
In the UK the 'street' level floor is called 'Ground Floor', whereas in the US they simply call it '1st floor'. So it depends on whether it's a British lift or an American elevator. See more and even more.
There are similar differences with many other words. One billion (historically at least) used to mean:
UK: 1,000,000,000,000 US: 1,000,000,000
It's one thousand times quicker to travel billion light years if you leave from the US! (Unless you are travelling million light years at a time.)
Within the U.S. it is common that when all entrances to a building are on the same level, the level above that will be called "2". In buildings which have entrances on two different levels (typically, though not always, because they are built on hills) it is pretty common to have the upper of those two levels be "1" and the one below be "G"; such numbering may apply regardless of which level is used more often as the entrance.
Additionally, if a building has many similar above-ground floors, but the floors at or below ground level are very different (e.g. if a hotel has guest rooms on all of the upper floors, public accommodations at ground level, and staff facilities in the basement) the upper floors will often be identified with numbers starting at "2", but the ground-level floor will be called something like "G" because it is fundamentally different from the numbered floors. A hotel with two public-accommodation floors might call them something like "G" [Ground] and "M" [Mezzanine] and then number guest-room floors starting at "3".