Hi there,
Do you have a bank statement to prove that £70 was taken out of your account? If so that's great. Furthermore, if you know where the test centre is, I highly recommend visiting in person and explaining to them of your current situation, using the bank statement as proof, if you have them. However, before you do visit, give them a call and try again, explaining to them that you have proof that £70 was taken out of your account from them. And if they still don't have any details, visit them in person.
Also just to note, not every university requires you to have taken the LNAT, unless of course you are aiming to attend a university where having completed an LNAT is one of the entry requirements. So if you don't take the LNAT, that's fine. You can still attend a university and study law. However, I'm mainly worried about the £70 you paid, despite not receiving a confirmation email.
I hope this helps. If you would like any further advice, please don't hesitate to message me.
Best wishes,
Narusha
Coventry University Student Ambassador