Once he reaches 3rd level, he becomes immune to the disease...and Lycanthropy is specifically mentioned, so, yes, he would be immune to it.Question is.. he was bitten while he was still 2nd level... is he still afflicted?
If you're looking to use Lycanthropy as a plot device, there are options available:
--You could ignore the immunity and have him still being affected, but that will likely make the player unhappy as you're throwing one of his class abilities right out the window. If you go this route and want him to become afflicted, then you should give him another ability in return for striping him of his Divine Health. If you go this route, the onset could be delayed for weeks or maybe a month or so. Maybe if he is able to find the rat that infected him (if its not dead already), or the rat that infected the rat that infected him, he could be cured. Racing against the clock to solve that problem before the paladin changes could definitely add some excitement to the game.
--You could keep the disease in his blood. Maybe he doesn't change (so long as he remains a paladin), but he could still potentially infect others. He could still be vulnerable to things like wolvesbane, but is otherwise asymptomatic. This could keep him from marrying and having children and really develop the unrequited love aspect of the paladin class that was mentioned in depth in the 2e Paladin's Handbook. It's an older edition, but still a good source for paladin stuff.
--Maybe other lycanthropes will recognize him as one of their own, even if he is no longer susceptible to lycanthropy. It adds to the roleplaying aspect of the game, but won't screw with the character's class abilities. This option would also enforce that he toes the line as a paladin by serving as a constant reminder of the consequences of him straying rather than risk losing his powers and transforming into a rat.
I guess I would have wanted the PHB paragraph to say whether any current conflictions were removed or not, but I guess they couldn't think of everything...I just know the player will object due to Divine Health, so I wanted to find out how to interpret the rule. In any case, I would like to level him to 3rd so as not to alert him just yet. I won't take away from him the paladin abilities or give him the wererat special qualities before he finds out either.
Keep in mind though that the Divine Health makes him immune to diseases and if you go ahead and give him the lycanthropy when he has just become immune to it, he'd have every right to complain--unless your game is set in Ravenloft where even paladins are not immune to lycanthropy. But his immunity should stand in any other campaign. That means they no longer affect him. If he hasn't had his first transformation by the time he levels up to 3rd, the disease should not work on him at all, and if he has had his first (or a few) transformations since, then he would no longer be a paladin. The writers didn't have to put in that it gets rid of existing diseases because the phrase "becomes immune to..." covers that. The paladin becomes immune to diseases, all diseases. Immune; not susceptible or responsive to. In the case of becoming immune, he would no longer be susceptible or responsive to lycanthropy.
Probably the best thing to do is discuss it with the paladin's player before the next session. Tell him he blew his save so he is facing the possibility of becoming a wererat (if you disregard his Divine Health). Tell the player the options you are considering. Ask the player how he wants to play this out. Ask him if he has any suggestions. Players are the ones playing the game, they should have some input when it comes to character altering, class altering events in the game. Maybe he (or she) will surprise you and come up with a good solution. Maybe they'll want to play the wererat thing out.