So, who pays for the first date? Details below?

We had matched on a dating site, and we messaged one another a bit. I ended the first conversation by saying, I had to go but I would love to meet him, and perhaps have lunch with him or something like that. He agreed and said he'd love to. Now being I was the one who mentioned a date to meet, should I pay? It was my idea but I dont know what dating standards are like now.

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Thanks for all of your comments and help. I have decided to go for paying it myself, but if he should be the one to pay it all, I will at least leave the tip. I'm not sure about what he would do as this is the first time I will see him.
For those of you saying that this is not a date, well, I disagree. We saw one another on a dating app, and he was texting me for a long time once, and I just told him it'd be great if we got to see one another and have sushi. He also added a walk with that.
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Also, for those who insisted that this is a meeting, and not a date--well--you do meet one another one a date. And I'm afraid Meriam's dictionary of a date differs with you:
date 1 (dāt)
a. An engagement to go out socially with another person, often out of romantic interest.
b. One's companion on such an outing.
So, who pays for the first date? Details below?
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