The Lost Tower is a place where trainers can mourn their deceased Pokémon. It's home to various Ghost Pokémon and at the top you will receive two items from the towers overseers
In Diamond and Pearl, there is really only one reason you need to go here, and that is for HM04 Strength. There are a few other items here, but the trainers are fairly weak, so grab what you need, battling the trainers along the way. On the fifth floor you will see two old ladies. One will give you HM04: Strength. The other lady will give you a Cleanse Tag. This item, when held by your lead Pokémon, reduces wild Pokémon encounters by 50%. You're done here for now, so go ahead and head on out!
In Platinum, you won't get Strength here so it's optional to go in here but do grab the ghost Pokémon in here. If you do decide to go up you will need Defog after 2F
Go south of the stairs into the southeast corner to find a hidden Stardust (Diamond/Pearl only). Go back towards the stairs and make the 2nd left to find Youngster Oliver and an Oval Stone. Head to the northwest corner and go up the stairs.
Follow the path south and to the west and you will run into Roughneck Kirby. Grab the Revive next to him then head north of him to find Pokéfan Leonard. Go to the northeast corner to go up the stairs.
Go south of the stairs and you will run into Pokéfan Rebbeca. Just south of her is Belle & Pa Beth & Bob. Continue West and you will find TM37 Return. Head north and just south of the stairs is Young Couple Mike & Nat. To the right of them in between the two gravestones to your right is a hidden Great Ball(DP). Go back towards the Young Couple and up the stairs.