You will only have one opportunity to move Dylan from his comfy chair under the umbrella, and it will occur sometime after you have talked to everyone else about him, and possibly after you gain access to the upper room.
How do I get into the room I can see above the pillars?
When you talk to Dylan after this, you'll have the option to ask him to help you distract Lily. He first asks you to talk to Abdullah for him, which you should do; it won't work, but what the heck.
When you come back, it's clear that his skills as a Lily-distractor are pretty minimal, but it does get both of them out of the way long enough for you to search his bag.
Later in the game, after you find the second tomb area --
Finding the Second Tomb
-- Dylan will be gone from the site completely. But he takes his bag with him, so there's no reason to return to his chair after that.