After two days of trying, a miracle this morning and I got through to Lazada customer care on the first ring of the first call. They told me that their engineers acknowledge that there is a problem with Lazada Thailand and they are working on it. They ask for our patience while they resolve it. After living several years in Thailand I have lots of patience. In my case although I can't login from a PC, the android mobile app reported my account as frozen, not locked, and allowed me to unfreeze it with an SMS code. However, although all my account details appear to be correct, the Order history and Message history have disappeared. I reckon there could be a risk using the app so I'm going to wait until Lazada give the all clear before doing any more shopping.
I discovered my account was locked on Saturday and curiously I received an email from Lazada that morning refunding my last order because of late fulfillment by the seller. That's the first time I've had a refund, I wonder if it somehow triggered the problem with the account.