A few points
Firstly, most phone banking I've done before has used the system when you phone up that the call-centre operator asks for your (for example) 3rd and 7th letter of your password. The computer decides which letters they are going to ask for, and only shows them those letters. Given the volume of calls handled, and the lag between successive calls from a single customer, it would be incredibly hard for a member of staff to get to see someone's password. Of course, LTSB don't seem to do this.
Now, I'm going to have to say, I'm not in the least bit surprised. A few years' ago, I dropped LTSB like a sack of spuds. Since the merger between Lloyd's and TSB their service had gone down the tubes, resulting in me suing them for about £5k, and then switching to HSBC Premier - the best banking decision I've made in a long time. Let me give you a few examples of just how bad LTSB have been. I've had my address revert to an old one in the computer without my intervention, and all my mail go to an address 3 or 4 moves ago. Then when I went to fix it, they spent an age telling me I had to go to my home branch to sort it out (despite having a home branch of convenience in London because I moved around the country so much). The best one they did was shortly after the merger though (late 90s iirc). I phoned my branch manager up to arrange an increased overdraft for that month. He agreed to it, but apparently didn't action it on the main computer. They had just implemented a new collections department where accounts that went over the overdraft limit were transferred. My account went in the red (according to the old limit, but fine according to the new limit that hadn't been actioned), and got transferred to the collections department, who promptly cancelled all my direct debits and started bouncing everything. When I phoned my branch, they accepted the error, but said they couldn't do anything since they had no control over the account whilst it was in collections. When I spoke to the collections department, they refused to accept the error, and wouldn't do anything for me until my account was back in order. I had to wait until the end of the month for pay-day to get my account back in order and transferred back to the branch, and then spent a year getting all my charges refunded (including charges from people who had their Direct Debit refused by my bank).
I would have changed my account almost immediately, except back in those days it was incredibly hard to do, so I vowed that as soon as I got a decent bonus I would switch so LTSB never saw a penny of my money. Of course, switching became easier, and I went through on my promise. Personally, I would never ever recommend anyone uses any service LTSB have to offer. They have no idea of customer service, and are a dreadful organisation. I would prefer to put my money in a rugby ball shoved up my fudge tunnel than ever trust that barrel of snakes again.