The Lakers should offer Lance Stephenson the max because Indiana probably wouldn't be able to match. Consequently either the Lakers would then secure Lance's services or they'd cripple the Pacers' financial flexibility and possibly earn themselves some free money when Indiana is forced to pay the luxury tax.
It's very straightforward. I think the argument that Lance Stephenson is worth the financial investment is similarly straightforward. I'll give it to you in 6 parts:
1). Lance Stephenson is a very good basketball player
Despite playing in a wretched offense with bad spacing, Stephenson shot 49% from the field in 2013 including 35% from behind the arc. He rebounds exceptionally well, he passes well, and at 6'5" 230 pounds with a 6'10" wingspan he can guard multiple positions along the perimeter.
It's very easy to build a good backcourt around Lance. His point guard needn't be an excellent distributor because Stephenson can share that burden. He also provides the floor spacing and defense that often disqualify other players from seeing heavy minutes in all situations.
Anything you could want in a foundational backcourt piece, Lance Stephenson provides.
2). Lance Stephenson plays a position where there aren't many superstars
Yesterday's shooting guard heroes are not the impact players they once were. Dwyane Wade just made a convincing argument that he's no longer a max player or a foundational piece of a championship team. Kobe Bryant hasn't played basketball in a while and the last time he was seen he was being described as a "DH." Manu Ginobili provides brilliance in short sparks and likely won't for too many more seasons.
While the NBA is chock full of elite point guards, not very many teams currently have excellent shooting guards that are worth building around. A team with a great shooting guard then has a sort competitive advantage over the rest of the league.
Right now if you went by numbers rather than reputation, you'd probably have to rank Lance Stephenson as the 2nd best shooting guard in the NBA behind James Harden.
If you expand the list to "2-way wings you can run offense through" he'd still likely end up in your top 10. He'll definitely be in the top 10 or even top 5 for the next four years of his career. Is it worth offering one of the league's ten best wing players a max deal to ensure he's on your team? I'd say yes, especially if you have lots of cap space and few good players.
3). Lance Stephenson is 23 years old
In general, I'm not a fan of investing in perimeter players long-term. Too many of them rely on athleticism and health that becomes awfully shaky when they reach 30. The number of guards who either have the skills or develop the skills to thrive when they get older are too few.
The ones that do match that description are either very competitive and driven, like Kobe or MJ, already relied more on skills than athleticism like Steve Nash, or have great size like Jason Kidd (who was also skilled and competitive enough to evolve his game as he aged).
Lance actually matches several of those descriptors, but it doesn't really matter because he's only 23 years old anyhow. If the Lakers (or someone) signed him to a $60 million deal for 4 years he'd be 27 when it concluded with potential to even get better as a player before or after the deal is done!
This is not the big risk some people are suggesting.
4). Kobe Bryant is donezo
Kobe had already lost his ability to be a good, much less lockdown, defensive player before he ruptured his Achilles tendon. Now he's pushing an old body to recover, which is a method that often results in more injuries.
It's very likely that the days of Kobe having a full, healthy-ish season are done. Even if he does come back at or near the level he was at before the latest injury, he could co-exist on the same team as Lance.
Kobe is also big, he's 6'6" with a 6'11" wingspan. You could assign Kobe the task of guarding either an opposing small forward or the least threatening offensive player in the opposing back court. Thanks to their combined abilities to handle the ball, the remaining guard for the Lakers could be a limited sharpshooter to help with spacing.
One thing's for sure, Kobe Bryant isn't dragging any teams to the playoffs in the West, much less the Finals, without considerable help from his teammates. He couldn't do it without a Center when he was a younger man and he certainly won't do it without considerable help as an elder.
Lance Stephenson makes the Lakers a legit team in the short term and gives them a backcourt piece to build around whenever the time comes to send Kobe out to live on the farm.
5). The criticisms of Lance are foolish
"Lance Stephenson talked trash to LeBron James and blew on his ear during a game! You can't give a max contract to a guy like that!"
This is just foolishness. Tony Parker had an affair with a teammates' wife at a much older age than 23 and I'm pretty sure the Spurs don't regret their investment into his contract. If Stephenson is a bit over-exuberant and childish while being a fierce competitor I'm not terribly worried. I'd be more worried if he was failing to improve as a player or if he was doing this while playing ineffectively.
"He hasn't proven anything!"
If you wait for a young guard to prove he's worth a max contract there's a good chance that he'll be past his prime when you finally offer it to him. The Rockets demonstrated the proper way to do this when they signed James Harden to a max deal.
Harden hadn't carried a team before, but he'd played excellently as a 6th man for OKC and carried their offense at times during the NBA playoffs. That's about as much as you're likely to see from such a player before they break out in a starring role.
6) Lance provides the Lakers with a plan
I'm not sure the Lakers have a plan right now. They are paying Kobe $25 million per season to tweet his wisdom to the world and shun his teammates, they're paying Nash $8 million per season to make thoughtful documentaries, and they just drafted PF Julius Randle with the 7th pick in the draft.
The smart play would be to embrace the youth movement and find some youth worth building around. Randle may or may not be a piece of the puzzle, Lance could definitely be a key cog on a contender. He already is, in Indiana. If the two of them pan out, all of a sudden the Lakers become an attractive place for free agents in 2015-16.
Do you know who's a free agent in that offseason? Potentially: Kevin Love, Goran Dragic, Ricky Rubio, Rajon Rondo, LaMarcus Aldridge, Kenneth Faried, Tyson Chandler, DeAndre Jordan, Nikola Vucevic, and some other worthy pieces.
The following year you see Kevin Durant and Russell Westbrook on the open market.
If the plan is to attract free agents or forced trades to LA, which has been the traditional path to greatness for the Lakers, then acquiring a piece like Lance Stephenson is the way to go.
If the plan is to suck and get more draft choices then by all means, let Indiana or someone else have him. Personally, I'd go with option A and go get Lance.