When you arrive in Tamur, make sure to buy new equipment for everyone (you can fore go buying Alex the Great Sword since he'll get a new soon enough). Whatever you do though, make VERY sure you buy Kyle the Wind Sword and not a Great Sword. Why? Cause it's ALOT better. After this, chat with the townsfolk and make a mental note about the guys who wants you help him lie about his "new medicine". Once you are ready walk north as if you were gonna leave the town.
When you reach the north entrance/exit to the town, you'll meet Laike again. How fun! He admits he knows not where to find the Black Dragon, but he knows how to get you flying again. This of course happens to involve a smelly, cranky and persnicktey old inventor named Myght who lives in a tower nearby. The only hitch, is that he doesn't like social interaction and large groups of people make him uncomfortable. Which inevitably means that Laike and Alex have to go alone. If you are ready, and if you listened to me, you should be, choose "I'd love to go." Everyone else will head off to the tavern for some of that famous Tamur Tavern Ale. In the mean time, it's you and Laike. So, head north to exit the town and head for Myght's Tower. (If you for some reason are not ready, you can turn him down and he'll go to the tavern to wait for you. Good thing too since you can't progress until you accept offer. :P)
Once you leave town, the tower is north-northwest of Tamur. Walk there, and enter the tower. When you arrive, you enter in floor one (I know it sounds obvious, but hey, I need a reference point, hehe). You'll find that when you enter, there are 3 doors. The 2 on the left and right go into the same room. You'll come out of there later. For now, talk to the person standing in front of the door in the middle. He recognizes Laike and greets him like an old friend (If you had turned Laike down and travelled here for fun, he would have been much less cordial). He of course lets you pass. Head up the stairs. On the second floor, you'll find a really annoying puzzle if you don't know anything about Astronomy. You have to walk in the four doors in a specific order. To save you the trouble, the order is: Planet, Star, Sun, Moon. Why is Moon last and not Sun? Cause this is LUNAR of course, hehe :P When you walk through the last door, you'll find yourself in a highly confusing maze. I'll do my best to explain it for you.
Upon emerging through the Moon Door, You'll find yourself in a rather large network of elevators and pipe tunnels. You need to know, that the elevator on the left goes UP only and the elevator on the right only goes DOWN. So if you fudge up, you'll have to start all over, so pay attention.
From the entrance to the third floor, go to the left side and take the elevator up to the top floor (3 times) and enter the door. When you enter the door, walk north and when you come to the T-intersection, go right and make your way to the door on the far west side. Either route will take you there, but the northern one is much shorter. Regardless, make your way to the door, and enter it.
When you emerge, you'll find yourself on the right-hand side of main chamber on the top floor. There are 3 doors on this level and you should have just came out in the middle one. Walk over to and enter the door on your left. When you enter, you'll find yourself in another pipe tunnel. Walk north and follow the path until it bends around and starts heading south. Take your first left and then north again. Follow this path until it turns south, and take the path to the left. Now walk left (or west if you prefer) until the path comes to a T-intersection that runs North and South. Take the north path again, and you'll nab treasure chest that contains a Crystal Sword, which you should of course, give immediately to Alex. Now walk all the way back from where you just came so you are back in the main chamber since this path leads to a dead-end.
Once you are back in the main chamber, walk all the way to the east most door and enter it. Again, you'll be inside another pipe, this one happens to be fairly simple. Walk north and take your first left. Go until you come to a chest. Grab it for a Healing Nut and then backtrack a tad so you can continue to the west to find the exit.
You should emerge on the left side of the main chamber on a platform with a door to your right. Go ahead and enter it. Once inside this pipe, you'll note that this is the first one you entered back when you started. Make your way all the way to the east again and emerge in the main chamber again. Once in the main chamber (you should come out in the middle door again), walk over to the elevator and ride it down twice. Step off the elevator and you should be on a platform with 2 doors. Take the one on the left.
Once inside, follow the path north and it turns left. Follow it until you get to the second path heading south. Turn south and take your first (and only) left again to nab a Silver Light from a chest. Go back the way you came and enter into the main chamber again. Elect not to take the door on the right, and ride the elevator down to the main floor of the chamber. Walk around to the left elevator and go up 2 times. Walk west (you can go under the overhang above you) and enter the door.
Follow the path north and around to the east. Continue east until your second path going south. Follow that path to grab another chest for a Barrier Ring. Walk back to the 4-way intersection, and go right. Continue on the east path to find the exit after taking the next north path. This puts you in the main chamber again. Walk all the way to the right and take the door there.
Just make your way west in this chamber (grabbing the chest along the way for 500 S) and you'll emerge in the main chamber again on a platform with a door to your left. Enter that, and you will find yourself in Myght's Laboratory....congrats! (^_^)
When you enter the Lab, talk to Myght for a rather funny video sequence (and only cause he farts at the end, hehe) and then him and Laike start talking. Myght catches on pretty quick that you want an airship. After being a somewhat stubborn ass, he agrees. Laike then tells you a "rumor" that the Black Dragon could be south of Tamur in the grasslands of the Prairie Tribe. About time he spilt the beans. Laike decides to stay and catch up on old times with Myght, so talk to Myght's Lab Assistants and then enter the door on the west side of the Lab. This is an express slide down to the 1st floor. You'll emerge in a room where you can go right or left. Both go to the room where the guard is, so take your pick and walk back to Tamur.