Generally what happens with any major Japanese band concert like this, is that presale tickets are offered to fanclub members on a lottery basis, as you mentioned. The 'lottery' part of it comes in because a fanclub member doesn't know if they'll win the chance to buy a really good ticket, or just an offer for a really crappy ticket. As you said, whatever isn't taken in the presale (and I don't believe they put all tickets in presale) gets released on the Lawson-listed release date.

If you can't get tickets from Lawson, there are ALWAYS locals lobbing spare tickets off online, for example two girls in the fanclub enter the lottery to see who gets a better chance at tickets, then sell the ones they don't want, OR foreigners living in Japan, who buy tickets to sell online to people such as yourself XD