Buying outside of Japan through the official agents listed on the official museum site is more difficult, as these agents only get allotted a small number of tickets.
i.e. these foreign agents (usually JTB) would be sold out for the month when Lawson online site says available. Well reported on various travel boards.
The English "cheat sheet" posted on the official website is inaccurate and essentially useless, probably wasn't updated for years.
You can ask your friends in Japan (if any) to buy for you, or hotel concierge (add ~1000 per ticket), online shops (check tripadvisor forum, for example)
When I went maybe 2 years ago, tickets were available on select time slots within the week via online or loppi machine - they have the same inventory and it's real time.
The museum (just a tiny western style mansion) was packed. The gift shop was the worst - more crowded than rush hour Shinjuku Station. Awful experience, probably because I am not a huge Ghibli fan to begin with.