Once your dog has accepted the Sit, Stay and Come commands, he is very likely ready to move on to Intermediate Training. At this stage, teaching him to Lie Down on command is probably your best option simply because he is already familiar with the Sit behavior.
Choose your treat, command your dog to Sit and move the treat towards the ground. Each time, move the treat a bit closer to the ground prior to allow him to take it. Continue this process without allowing him to move from the Sit position. If he gets up, be patient -- this may take a bit of time. After he has mastered the first move, try moving the treat a little farther away but still keeping it on the ground. Now, in order for him to retrieve this goody, he must Lie Down. Now is the time to use the command, "Lie Down". Be consistent with this technique and eventually fade out the treat.
You must communicate to your dog that pulling on his leash is unacceptable. Good manners are a must and lunging and jumping at other people or pets is simply bad behavior. Begin teaching him to walk next to you by making small circles, walking very slowly. Change from walking to the left to walking to the right. Eventually, there will be total slack in the leash. But hey! Once in a while, allow him to smell the roses. Every dog loves to explore and your baby deserves this treat occasionally.
After your little friend is consistent with the Sit behavior, training him to Sit Up is a snap. Choose a bit of food or his favorite treat, hold it over his head while he is in a Sitting position but low enough so that he can reach it. Continue this maneuver but raise the treat a bit higher each time so that he must stretch for it but still remain seated.
Now, you must hold the treat higher yet. Uh oh, he won't be able to take it unless he raises his front paws from the ground. At this point, use the verbal cue, "Sit Up" and immediately reward him. Very shortly, he will understand what is going on and you may fade out the treat gradually, use only your hand and give the cue "Sit Up."
Teaching you little pal Intermediate Behaviors is going to be a very rewarding experience, both for you and your dog. Remember, patience is the key and loving and accepting your pet will cause him to want to please you. Enjoy the time you have together.