So, what makes a good hook between players?
Assuming that you want to use connections between players to drive play, then this puts an interesting question to the player: What sort of thing would they like to see happen? Normally, this is something that the GM needs to pick up on and fold into the game, but since we're talking about lateral play, this is an opportunity for the player to think about this a little more concretely. Some players won't like doing that. If so, then just don't sweat it - this is an idea for people who want to try lateral play, not for imposing it on people who don't.
So, the obvious place to start is in the character's background. Odds are good if you're interested in lateral play, you've put some thought into your character, so there should be some material to work with, unless you've made the cardinal mistake of writing a resolved background (that is, a background where all the interesting things have already happened to the character). If you've done that, or if you don't have a lot to work with, then you might need to build some ideas from scratch.
Thankfully, whether your building new ideas or rooting through existing ones, the general model is the same, and based very much on a trick I've talked about. The temptation for lateral play is to create connections between characters, but that solves the wrong problem. You want those connections to be the _result_ of play, not causes. It may seem counter-intuitive at first, but I think it will become clear.
What you want to do is find an external thing (A person, a cause, a location, an idea) that both characters are invested in, then make that the rub of the plot. Seems simple on the surface, but that raises a question: how is that a lateral plot rather than just an external plot with multiple hooks?
The trick is that the characters need to have different kinds of investments in the subject. That is to say, they need to have different relationships with it and (more importantly) different needs from it. Provided that one character has a strong enough need to be a hook, that will draw in the other player as the subject is engaged.
To do this well, I'd usually suggest that one player have a passive, positive relationship with the subject (that is, be happy enough with the status quo to not be looking for a change) and one have some element of tension (that is, there is something they want or need). I would suggest against making that want or need something that harms the subject (unless you're really comfortable with direct player conflict) but rather make them want or need something that is, in turn, a step removed from the subject. As such, the active player wants something of (or from) the subject, but isn't necessarily threatening the subject itself.
This is easy enough when talking about concrete subjects (Ser Reginald is Orlando's old duelling instructor, and they chat at times. Davis needs Ser Reginald's approval to marry his daughter. Bam, instant lateral hook) but you need to be a bit more creative (or more straightforward) when the subject is more abstract. A simple example might be: Tom is an expert on Valisian artifacts, Anne needs to get past a Valisian Guardian statue to get a widget. A more complex one might be Tom's family made it's money in the slave trade. Anne needs to find someone who might have been sold into slavery.
In each of these cases, the trick is that the active player (the one who wants something) is in a very normal play position - they want something and need to take action to get it - but the difference is that rather than the GM introducing NPCs or resources that could help, the GM stays clear. The tools needed can be found in another party member, and it's up to the players to find their way to that.
It's not a foolproof model. There's always a risk that some ideas will get dropped on the floor, or go in unexpected directions. But it's a simple enough structure that it shouldn't be hard to rope in players willing to give it a shot.
[back] 1 - Expertise is an interesting point. One other way to create a lateral hook is to have player A need expertise player B has to solve problem C. This can work very well, but it's not well-supported by some systems. In the absence of some real mechanical hook for expertise, this can be an unconvincing hook, so I mention it as useful in specific cases, but not in general.