I think AL's reaction is explicable if the questions DV was posing were touching on stuff he'd rather forget about SJL and her hinted-at but undisclosed other life. The more I think about it, the more it seems obvious that is where the solution lies (but that it's clearly now too late to get there).
All we really know about this aspect of her is that it was racy enough for the family to want it all downplayed, and indeed to withdraw support for AS' book when it looked like coming up. I think their comment was "We do not recognise this portrait of our daughter".
Of course, if SJL did indeed have a collection of mystery men in her life, this was acutely relevant to solving the case. It doesn't look like she was forcibly abducted by a stranger so the assumption is that it was someone she knew. The male coterie is the obvious group among whom to look for a culprit.
But at the same time, disclosing this could have been a massive setback to the investigation. At that point, the news story changes from 'nice middle class girl disappears' to 'slapper murdered'. One senses that the Lamplughs would actually have preferred the case not to be solved at all than to have this mystery life exposed and have this be the story.
And maybe AL feels the same. Assuming as I think we can that he was genuinely fond of her, I can't think why he'd welcome anything coming out about her now that would be seen as discreditable. She's remembered as a mystery whose disappearance created something good, the trust in her name. She is not remembered as a trollop who had it coming.
It is perhaps analogous to the situation 30 or 40 years ago when some famous chap would die, it would then emerge that he was gay, and the family would deny it or say could we please not talk about it. Nowadays nobody cares, but back then it was discreditable.
AL's reaction in the book still seems odd to me. The questions DV put to him were not hinting at Suzy's potential 'other life' but rather about the last time he saw Suzy, the weekend before she disappeared.
Now this might still be an upsetting memory for AL to remember, and rightly so. However, he did agree to be interviewed by DV and he must have known that potentially there was going to be some awkward or upsetting questions he would face.
If he felt this way (which his reaction to the questions seems to show), why put himself through it and agree to be interviewed in the first place? What sort of questions did he think DV would ask him?
This is JMOO of course but I do wonder if the following happened that weekend.
In an old documentary AL said the Friday night at Mossop's and then at the pub round the corner (presumably the Prince of Wales) had been a pleasant night out.
However, I do wonder if this actually was the case. As we know when AL was on holiday Suzy had apparently got herself a new boyfriend, so on this Friday night out did she tell him about this new man in her life, and the evening did not go as well as AL had said - maybe they had a disagreement and that's why they didn't go to the pub?
On the Saturday evening Suzy went to a party but AL wasn't invited (maybe because the new BF was there?), and on the Sunday Suzy went with her friends to Worthing that afternoon. AL did turn up but had to make his own way there and back. So that Saturday and Sunday it doesn't appear that Suzy wanted to be in AL's company much at all.
There was supposed to be a phone call that night around 10.15, but AL said he couldn't remember if Suzy called him or he had called her. It was supposedly about meeting up with friends on Tuesday night, but how do we know this for sure? Suzy wasn't around to tell the story, so for all we know it could have been AL getting angry with her for snubbing him that weekend.
So did DV's interview with him bring this all back, that maybe things were not so fine-and-dandy between him and Suzy after all? Hence his reaction by storming out of the meeting with DV and Caroline.