@Ivan ***********
Ah, I see your problem. You're trying to use Lazada Wallet to check out. And that does indeed require a Thai ID card.
Fortunately, Lazada offers many other options for payment, one of which is to use a debit card. No need to use the Lazada Wallet.
When you check out, you get to the payment part and you can pull up a list of options, as shown in the attached screen grab. The first time you do this, go down to the "Credit/Debit Card" option. There you enter the details for your Thai bank's debit card.
You can choose to save the card to your Lazada account, as I did, and all the details will be remembered for faster checkout next time. Easy!