You could always touch his hair and face.
How do I turn my boyfriend on while sitting in his lap?
Squirm!
The most obvious way to turn your boyfriend on while sitting on his lap is to move around very slightly so you're rubbing up against him. Having said that, this may not work and you shouldn't worry too much if it doesn't.
Every person is turned on in slightly different ways. Many men would be turned on by a woman they find attractive moving around on their lap. But this isn't always the case.
Some people are more visual, for instance, and may be more turned on by simply looking at you in a certain outfit or position. Just because they're not turned on by you in one way, doesn't mean they're not attracted to you.
Other issues
People can find it difficult to be turned on if they're overly stressed, unwell, or if they've already "relieved themselves" very recently. I'm pretty confident, however, that you'll achieve your goal if you wriggle around slowly.
A guy's "lap area" is very sensitive, so it is likely you won't have to do too much rubbing up in your boyfriend's lap before he gets turned on.