training a two year old to lunge

Hi so I was helping another friend train her horse a beautiful but stubborn blue roan gelding. He knows how to lead, and stand when tied. So we were trying to train him to lunge and he caught on very quickly and was doing great at a walk but when I asked him to trot, by tapping his rump with a whip and kissing to him, he stopped. I asked him to trot again and he just half-reared and started going backward.
What should I do?

I wouldn't be lunging a two year old, but if you HAVE to.

It is best to teach lunging in a roundyard. I prefer to free lunge initially, so that the horse isn't worrying about being restricted by the rein. Just teach him how to go and stop with your body language and assistance of a lunge whip if required.
The most important thing in lunging is that the horse goes forward without restriction and without baulking.
So when he goes to jack and rear, immediately drive him forward. First body language and voice aids, then try walking directly towards his rump (don't get yourself kicked), and if he still doesn't go forward, drive him with the lunge whip. Don't be scared of giving him a solid whack or flick - often just cracking the tail of the whip will be incentive for the horse to go forward without even touching them.
It is just vitally important that you NEVER allow the horse to resist forward movement, as this can and does lead to rearing.

We tried giving him a solid thwack and he started half- rearing.

Well then give him an even solider whack!! Do NOT let him get away with it. You have just trained the horse to rear.

My friend is very protective of her horse and would go up to him and stroke him and beg him to behave. I know this is wrong but I don't want to boss her around. If he were my horse I would give him a stronger swat but since he's her horse I don't know if I should. What should I do?

Thats up to you and your friend to work out. Maybe direct her to the forum so she can see other people's opinions of babying a horse.
Horse's don't need a cuddle buddy, they need a leader. By babying him when he baulks, she is purely reinforcing his behaviour. Horse's learn from the release of pressure. So you put the pressure on to ask him to move, he baulks and rears so you stop putting pressure on and give him a pat. He thinks "GREAT! I did the right thing, when mum waves a whip at me, I just need to stop and rear to remove the pressure". Then the rears get higher, more dangerous and it becomes ingrained in his thought process. Once you teach a horse that it is ok to rear, even just little hops of the front legs, you are setting yourself up for absolute disater.
Personally, I don't think your friend is asking for trouble having a young horse, without even knowing one the the most basic aspects of training.