The only way to keep LeBron in Cleveland is to have him win a title. The allure of playing in Miami with Wade and Bosh far outweighs his desire to stay in Cleveland. Even if he didn't go to Miami, he would still be mighty tempted to go to New York or Chicago. But if he wins in Cleveland then there's no reason to go. He would have a ring, have the adoration of a city begging for sporting success, and made a legacy as one of the game's all-time greats.
But how does Cleveland win? The first POD is Carlos Boozer leaving. Boozer was a rising-star in his own right in 2004. That was just his second season in the NBA, and he was already averaging a double-double. Let's say the Cavs pick up his one-year option before negotiating a long term deal. In OTL, Cleveland believed Boozer would come back if they declined his option. Instead he signed with Utah for more money. Keeping Boozer in Cleveland gives LeBron a strong wingman going forward. They had totally different skills and would complement each other well, much Jordan and Pippen. If Boozer avoids the injury bug, then the two of them could mature into a dynamic one-two punch.
The second POD is the 2004 NBA Draft. Luke Jackson never amounted to much, and was a waste of a lottery pick. Let's assume that the Cavs don't select Jackson but instead pick Josh Smith. They weren't going to pick a big-man, especially when Big Z is at his peak and they just locked up Boozer. Smith gives them great athleticism at small forward and elite defensive ability. This moves LeBron to shooting guard, not his natural position but he'll still be a force. With Smith in the fold, the Cavaliers starting lineup for the next year looks like this: Jeff McInnis (PG), LeBron James (SG), Josh Smith (SF), Carlos Boozer (PF), Zydrunas Ilgauskas (C). This is a solid starting group and one which has great potential going forward.
Obviously butterflies make it nearly impossible to predict what happens in the long term, as the draft lotteries and playoff results will be affected. But assuming that the basic arc of the NBA goes largely unchanged (i.e. the Celtics get the Big Three, Kobe stays in LA, etc.) than the Cavaliers have a great chance to win the title at some point with this core group. If they make upgrades in free agency and draft a little better, then they will be at the top of the power rankings around 2007/2008. With LeBron, Boozer, and Smith all playing great basketball, this group could very easily win a title. If that's the case, than LeBron stays in Cleveland and crafts a legacy as one of the greatest players of all time.