Lawson, Family Mart, Seven and a few others are chains of "conbinis", convenience stores.
In Japan, they are quite essential to modern life. I mean it.
You can go to the store for the essentials, like food, phone chargers, magazines, umbrellas and sweets. But also, they always have a ATM machine, so it's a stop when you need to retrieve cash and you can pay bills and billets there, directly with the attendant. The stores also receive packages for clients, since lots of people live alone and have no one to receive their packages at home. You can buy train and bus tickets there for long travels too.
And they tend to be open 24 hours or at least close to it.
So, due to their relevance in modern life in Japan, they are often scenarios for many plots in manga and drama, too.