You can select an option to use your Lloyds mobile app instead of receiving a phone call. It's not exactly what you asked for but it's a workaround until someone finds a better solution. That's how I do it myself by choice. I didn't know there even was an issue with receiving calls from Lloyds as I always used the app instead.
Here's what it says on the page when you try to pay a new recipient for the first time.
"Confirmation through our Mobile Banking app offers a quick and easy alternative to telephone validation.
Taking advantage of the security software built into the app, we will send a confirmation request to your mobile phone. Simply confirm your identity by entering your memorable information and approve the request."
I am facing the exact same issue. Contacted Virgin who replaced my sim and then tried logging in. Still no luck. Called Halifax and they say it's an issue with virgin.mobile. So I have tried everything by now and these companies just pass on the buck from one to the other. Wondering if you have had any luck?