Given that many of us here suppose SJL died when she went to retrieve her stuff from the pub, it's a very good call to consider exactly how it ever came to be lost there in the first place.
If I have understood correctly, we have it only from AL that the PoW wasn't one of SJL's regular haunts (and therefore, goes the inference, why would she have been there?). This may only mean that it wasn't one of her regular haunts when she was with him. We know from AS, however, that SJL was actually four-timing an unwitting AL with three other men when she disappeared. Some of these were apparently "FWB" arrangements, with no mutual expectations of exclusivity, but others including AL were not aware she was doing this. In the spirit of the old Royal Navy toast - "to our wives and girlfriends: may they never meet", if SJL wanted to keep matters in hand, she would have needed to keep each of these men away from one another.
It would take quite dextrous management to get away with this. There would be places it was not safe to go for a drink with AL in case she ran into any of the others there. Equally there would be places it was safe to go, because she was not going to run into any of the others. So conceivably, the PoW was one of the latter. It was her local pub and not one of which AL had a high opinion, so he was never likely to rock up there. This would make this place a safe one to visit with her various other men.
So is this what CV noticed - a good-looking regular, in the company of different men in constant succession? You can often tell from couples' body language if they were sleeping together. Did he notice her during his 12-week training stint, then notice her again on the Sunday night, then decide he needed some of what everyone else was apparently getting? So he lifts the stuff when she goes to make a phone call, so as to bring her back the next day when the pub's going to be empty?
The reason why CV's involvement is so mysterious is that if he killed her:
1/ he did so spontaneously in the course of a visit that SJL arranged with other people at the pub. He didn't organise this and can have had no expectation of cornering her alone, so when that situation materialised, on minutes' notice, he turns into an attacker then back into a relief barman without giving himself away.
2/ or, he reads the diary, decides she's a bit of goer, and demands sexual favours from her.
3/ or, he reads the diary, thinks "rich yuppie slag", and decides to demand money for its return; in which case, his partner could be complicit. No woman would turn a blind eye to her partner carrying out a sex attack on another woman, but if she herself was dumpy, plain and poor, she might be envious enough of SJL - who was none of those things - to acquiesce in CV's ripping her off.
In the first two cases, how was he planning to get away with that without killing her? It's impossible. The third seems possible, and could explain his partner's present-day hysteria on being approached (and CV's own, when he hears she has been).
The above also fits with some elements of what we already know. DL was aghast to learn of how SJL lived her life and we know she wanted it suppressed. AS indicates that at the family's request he removed the "News of the World" type of material from his book - but he still leaves in the four-timing, so the mind boggles a bit. Perhaps he suppressed how SJL's pocket diary tracks her meticulous and methodical management of her social and sex life to allow her to meet and sleep with up to four different men at a time, using specific venues to ensure their paths never crossed. The police rather awkwardly explained that SJL was "a modern young woman"; is that what they meant?
I'd always assumed that she simply stopped off to make a phone call on the way home to her mother's, but as Konstantin notes we've only got that from AL; and how that results in her losing her stuff under pub table several metres away is not clear. It seems possible that she was there with another of the fan club, or that her stuff was lifted, or both.