TL;DR: If you enter a fan club/general "raffle" (抽選):
- you enter the raffle;
- you get notified if you're successful;
- if you're successful, have a friend pay at a FamilyMart;
- pick up your tickets at a FamilyMart when you arrive in Japan.
If you buy a general sales (一般発売) ticket:
- you go to eplus and buy your ticket;
- you pay with a JCB card or have a friend pay at a FamilyMart;
- you pick up your tickets at a FamilyMart.
Being a big fan of Japanese music, I have been to a number of concerts in Japan. Here are some of my observations and experiences.
It's very hard to purchase tickets from abroad, unless the relevant parties consciously make it easy for people from abroad. Of the major ticketing websites (Lawson Ticket (L-Tike), eplus, pia and Rakuten Tickets, perhaps also Line Tickets these days), only Rakuten supports users from abroad reliably (since you can pay with international credit cards). l-tike even go as far as blocking overseas IP addresses.
It seems that tickets for the Nakano Sun Plaza show is not on sale yet, so take a deep breath. There's a fan club pre-sale, which will allow you to claim your ticket earlier and get you some better tickets, but you need to join the fan club to enter the raffle. If you want a good seat, consider that.
Almost all Japanese artists do a "raffle" before general sale. Some do two or more: one or more for fan club members, and one for non-members. FC members can enter the raffle early and thus have a higher chance to get a better seat (or any ticket at all). However there's no guarantee, everything is ultimately random.
If you do join the fan club (=FC), you'll login to your FC account, click on a link, and then enter the raffle through eplus (or whatever ticketing site the artist's management prefers). Keep in mind that joining the FC will cost you money too, usually a yearly fee of 2,000-5,000 yen.
After a few days, you'll be notified if you have been selected (当選) or not (落選). Depending on the artist, the selectivity can vary greatly:
but my guess is that LiSA concerts are not extremely popular, so there's a decent chance to get selected she's much more popular nowadays.
Remember to select the option to claim your ticket at a convenience store; this will save you so much hassle. The preferred convenience store chain of eplus is FamilyMart, BTW.
All the major ticketing outlets also provide e-tickets (QR codes) nowadays, but it is up to the event host whether or not to use them. If e-tickets are used, you will just need to download the ticketing site's app on your phone and show your QR code at the entrance. However, sometimes FCs do not allow overseas fans to join. Some require payment via a Japanese mobile carrier, and some require a Japanese credit card.
In some cases, FC tickets have printed names to prevent unauthorized resale. However, this happens almost only when the artist is immensely popular (think Perfume, Nogizaka46, EXILE, etc.), so I don't think this is likely. But if that is the case, you'd need to bring your passport to the concert. Some artists use facial recognition nowadays; you'll have to upload a photo to the ticketing site, and a facial recognition system will check if your face matches that photo.
After you get selected, you will have a few days to pay. However, AFAIK, eplus rejects foreign credit cards (except perhaps JCB and Amex cards), so if you don't have a JCB/Amex card, you'll need to have a friend pay for you at a FamilyMart in cash. If you don't pay in time, your ticket will be cancelled. I suggest don't even try using your card, unless you can confirm it would work otherwise. If you use a credit card and the payment doesn't go through, usually your ticket is cancelled right away, so do not risk that.
I can confirm that Rakuten Ticket accepts all major brand international cards, and eplus & L-Tike accepts Amex & JCB cards. I don't know about the others.
Then, when you arrive in Japan, go to any FamilyMart and claim your ticket at the FamiPort (ファミポート) terminal in the store. You'd need to type in the code sent to you via email, print the receipt, and give it to the cashier. The cashier will then print the ticket for you, and you're good to go. But IIRC the FamiPort terminal interface is Japanese only, so you'd need to be able to read that, or have someone help you with that.
Alternatively, if you don't want to enter the raffle, you can almost always buy a general sales ticket. Just go to the same website (eplus) and pay with a JCB card/have a friend pay, and then claim your ticket at a FamilyMart. Exactly the same process.
If you're confident, you can wait until you get to Japan and purchase the ticket at a FamilyMart. All FamiPort terminals are connected to eplus, so you can buy your ticket at one of those terminals and pay at the cashier. eplus shuts down online sales around 24-48 hours before the event, so going to a FamilyMart is the only way you'd get a ticket that late.
A reminder: the layout of Nakano Sun Plaza Hall makes it a bit hard to see clearly in the back, so getting a FC ticket might be worth it. If you don't care too much, I think it's likely you'd be able to get a ticket even after you arrive in Japan.
If you do this more than a few times and are sick of going to a convenience store every time, consider getting yourself a LINE prepaid JCB card. This can be recharged at Seven Bank ATMs and used just like any other JCB card.
There are "unofficial" ticket resale sites in Japan. Some artists are popular, and as such there's much more demand than supply. Technically, tickets cannot be transferred to another person, however since most tickets don't have a printed name, there's no way to know who bought the ticket. Even if there is, there's a way to work around it.
The largest resale site in Japan is Ryutsu Center, though they have blocked international customers due to troubles with them, so you'll need to have a Japanese address. The use of resale sites is not endorsed by this answer.