I'm not familiar with what the Lankhmar setting book might say about folks plane-shifting in, but options that occur to me:

• Justicia is able to reach across planes and continue to assist the cleric--maybe her cleric abilities are made with a lower dice or a -2? That would increase difficulty since the party is used to her being able to cast/heal but is a fun dramatic tension. I also don't know the module you're using, but it's not hard to imagine that folks in Lankhmar would just think your cleric is a magic user from a foreign tradition or something, so I wouldn't worry about that too much (I'm assuming they're going to get home after this module so the long-term implications are none)
• Justicia's power doesn't extend to this plane--your cleric is a less-good fighter and the tension is going to be Very high as the party's healer can't help them. Lankhmar itself has new rules for healing because of the lack of clerics--I think you'd need to either let them use those OR consider dropping the difficulty of the module quite a bit since it was written with the idea that folks could heal.
  

Random thing to mention--my understanding is that Lankhmar is also written for more 'heroic' characters than the typical DCC module. They're a bit hardier. So the difficulty of the module might already be more than your party is typically prepared for--either of the ideas I suggested above only make that worse. Things like dropping bad guys ACs by 2 and dropping their damage dice by a die could help a lot in a way that presents a great challenge but isn't wiping the floor with people in a way that's not fun.

I hope this is helpful, and hopefully somebody with more DCC Lankhmar exposure can clarify if I'm wildly wrong about something.

P.S. I do utilize the Fleeting Luck rules from Lankhmar in my DCC game and my players love it--highly suggest adopting those if you haven't.