In anything short of an impossible dream scenario (where Miami gives up the best player in the world in return for a fraction of his value) I wouldn't do it.
In the real world, for us to have even the faintest chance of getting Lebron in a trade we'd need to strip the team of every bit of future potential we have, including:
1 - Picks
We'd need to give up every 2014 first round pick we have. This is expected to be the best draft class in years, and if Miami are giving up a player of Lebron's level they will want every possible chance to pick up a future superstar (on a rookie contract) in return.
2 - Our best player
Firstly, Miami is weak at Point Guard. Secondly, Lebron is Miami's top ball handler and playmaker. Thirdly, Miami is not giving up the best player in the entire NBA unless they are getting AT LEAST one All-Star in return. For us to have any hope of getting Lebron, we'd need to give up Rondo.
3 - Our best scorer
With Lebron leaving, Miami would need a starting calibre Small Forward to fill the gap. I doubt a team like Miami (who is in win-now mode) would be willing to take a gamble on Michael Beazley's maturity. They would want somebody to fill the starting SF spot and to help fill some of the scoring void. I have little doubt we'd have to send Jeff Green their way.
4 - Our young talent
Even with all of the above, I seriously doubt Miami even considers this unless they get at least one talented young player with upside. With Bosh already handling the center spot I imagine they would want either Bradley, Sullinger, or (more lkely) both.
Now for argument's sake, lets say we gave all of that up. Lets say we sent out Rondo, Green, Bradley, Sullinger and all of out 2014 first rounders in return for Lebron. That leaves us with a starting lineup of what?
PG - Jordan Crawford
SG - Courtney Lee
SF - Lebron James
PF - Brandon Bass
C - Faverani / Olynyk
Some thoughts on that lineup:
1) It's not going to contend for a title
Lebron never won a title in Cleveland despite being surrounded with significant talent, and in Miami it took two extra superstars and a team full of quality vets (all willing to sign for well below their worth) to get him there.
2) Lebron is getting close to 30 already. We'd need to surround him with a willing Roster within the next 2-3 seasons to make this worthwhile, yet every bit of young assets we have would have just been traded away for him. We'd have no young players with potential (except maybe Crawford / Olynyk) and no picks for a few years. Plus we would probably be at least a playoff team, so our own future picks would be worth very little.
Honestly, I would much rather stick with what we have, which is:
* A relatively young All Star point guard who still has potential (Rondo)
* A trio of young players with medium-to-high upside (Bradley, Sully, Olynyk)
* A two-way swingman with great atlethicism who can score at a solid rate (Green)
* $25M in upcoming cap space (Humphries, Bogans, Crawford, Brooks)
* Multiple 2014 first round draft picks
* Multiple future draft picks (via Brooklyn) which could easilly become lottery picks
People don't realise we actually have a LOT of upside in the grand scheme of things. With the amount of potential Cap space we have coming up, I'm pretty sure we could sign Lebron straight up as a free agent if we wanted to. We'd actually have a much higher chance of that too, because me may be interesting in teaming up with guys like Rondo, Bradley, Green, Sullinger, etc. Especially given all of the upcoming draft picks we have, he'd have the opportunity to join a team that could contend for years to come.
On the other hand if he came over in a trade he'd be joining a barren team with no talent (because it was all given up in the trade for him). I seriously doubt Miami would trade him away to a place with such a grim future - they would probably keep him until free agency and make their best effort to re-sign him. I doubt they would trade him if they had even the slightest belief that they could get him to return.