Can you break doors by throwing things at them?

According to this thread (emphasis mine):

Something I've not seen mentioned is the fact that it's possible to demolish weakened walls and many doors. Obviously explosives will destroy them, but simply throwing junk at them gradually causes damage. Of course, boxes and extinguishers quickly break, but barrels are indestructible. Throw one at a door or weakened wall about a dozen times and it'll eventually smash through.

So, try throwing the fridge a few times, or finding an indestructible object like a barrel, and it should work.

This should also work for Lee's Apartment. Per the wiki link in your question (emphasis mine):

But when Jensen arrives at Lee's apartment in the Youzhao district by either hacking the terminal next to his door or breaking it, the apartment is empty.

From the same thread I linked above, it does not look like this requires any special augments (emphasis mine):

It's a pretty good way of saving Praxis points early game, you don't need to upgrade hacking to loot apartments when you can simply break the door down. If you keep your eyes peeled for cracks in the walls, you never need to spend the Praxis and energy to punch through them. It's of more use on a replay when you have an idea of where the handy weak walls are of course.

You could also try looking for a weakened wall (look for cracks), and then throwing the fridge at one of those (though I don't recall offhand if there are any weakened walls to get into Lee's Apartment.

Pretty much the only way to enter that door is to hack the console. Here is a wiki about this quest that does not suggest any other ways to open the door.

http://deusex.wikia.com/wiki/Shanghai_Justice

Simply put, this is a side quest, and completion is not required to complete the storyline. It is necessary to be able to hack the door open in order to complete this quest.

Also, there is no Augment that allows you to specifically break doors, and there are no weak points in the walls of that apartment that will allow you to enter without hacking the door console.

As I'm sure you've already found, there is an augment that allows you to pick up heavy objects (like the refrigerators, etc that you already mentioned.)

http://deusex.wikia.com/wiki/Cybernetic_Arm_Prosthesis

Most things that have the ability to be destroyed will let you know when you get close enough to them, others will let you know that they are indestructible. If you inspect this door, you should be able to find out if it is able to be destroyed, however I believe that this particular door and most doors like it are indestructible.