The Backstory
It's an inevitability that the NFL moves, at least one team, back to Los Angeles. Each of the three teams vying for a relocation to LA has previously called the City of Angels its residence.
The Rams (1946-1994) - The Rams left Cleveland in 1946 after winning the NFL Championship and brought professional football into LA. They saw extreme success in their early seasons there and won seven straight division titles in the late 70s. There were two issues, swept into one, that caused issues with the Rams in LA: location. The Rams played in the LA Memorial Coliseum, the largest stadium in the NFL with 90,000 seats. They could never sell out the stadium, though. This caused blackouts on TV. Also, the stadium's location in South Central LA deterred some from attending games because that area of the city was becoming quickly known for being a dangerous part of town.
In 1980, the Rams started playing in Anaheim Stadium and as the stadium failed to stay up-to-date with box seats and in-stadium revenue producers, the shopping process started. By 1994, the Rams secured a deal with the city of St. Louis and had a stadium in place to move the team and the Rams have spent the past 21 years in St. Louis.
The Raiders (1982-1994) - Al Davis took the Oakland Raiders to LA without the consent and votes from the NFL. He had a hairbrained scheme that the NFL was going to move to pay-per-view broadcasts and he would rake in millions from that decision. The NFL never moved that way. Davis moved into the LA Coliseum and kept working on renovations to improve the stadium. Where the Rams couldn't get the renovations needed, the Raiders made strides forward. Once the LA Sports Commission stopped further renovations to the Coliseum, Davis decided to make the move back to Oakland in 1991 and when the Oakland-Alameda County Stadium approved renovations, the move happened in 1994.
The Chargers (1960) - In one season in Los Angeles, the Chargers went 10-4 and lost in the AFL Championship to Houston before relocating to San Diego the next season. Where the Rams and Raiders built traditions and memories in San Diego, there isn't much memory of the Chargers in LA. The reason for the Chargers looking to leave San Diego is exactly why the Rams and Raiders left LA in the first place, outdated stadiums.
Current Climate
Each of these three teams has some issues in their current situations. As listed above, the Chargers stadium is highly outdated and has been an issue for the past 10-15 years. There has been little to no progress by officials, owners, and the league to make a new stadium happen in San Diego. It seems like there is no way that the Chargers return to San Diego for the 2016 season.
The Rams have the best current stadium out of the three but since Stan Kroenke purchased the Rams, the talks of their return to Los Angeles started creeping up. With plans of a new stadium in St. Louis falling apart and being deemed unsatisfactory to meet the requirements by the team and league, Los Angeles is a front-runner.
Most current reports say the Raiders will be on the outside looking in of this relocation. If two teams move and the Raiders are left out, then there will be a reimbursement of sorts for the Raiders. It'll likely come in the form of a guarantee to get a new stadium deal done in Oakland or additional incentive for a future relocation, possibly to San Antonio among some other cities.
Future Framing of the League
If the Rams move back to Los Angeles, there isn't much of an adjustment for the divisional or conference layouts. The Rams will be closer to all three teams in the NFC West, creating shorter travel time for three games each year. The counter-effect of this is how it creates longer distances for some of the Rams other five road games. Currently, the Rams are much closer to the rest of the league. When they have to play on the East Coast, it's a short trip. The difference should even out most of the time. Next year would be extra travel for the Rams heading to the Southeast for contests against the NFC South.
Both of the other two teams moving to Los Angeles would be very short trips from their current locations, staying within California. A move by the Chargers or Raiders wouldn't necessitate a divisional realignment.
The relocation that could cause realignment would be a move by the Raiders and Chargers into the Carson City joint stadium project. This would create two games with the same teams playing each other in the same stadium each season. It would also bring the Chiefs and Broncos to the stadium twice per year. The NFL likely wouldn't want to see two teams in the same division playing in the same stadium.
If the Chargers and Raiders moved to LA and the Rams didn't, then it would create a situation where a simple conference and division flop between the Rams and Chargers/Raiders would occur. This would put the Rams into the AFC West, which would be more of an AFC Midwest with teams in Kansas City, Denver, and St. Louis. The Raiders or Chargers would move to the NFC West and be in relative proximity to the 49ers, Seahawks, and Cardinals. This would cause a change in division rivalries and be the first changes made since the league realigned conferences in 2002.
Will the NFL work in LA this time?
As long as stadiums are built well and maintained then there shouldn't be issues for a team to thrive in the second biggest market in the U.S. The major questions revolve around how much there is to do in LA and if fans will turn out to see a team that isn't successful. All of the potential movers had losing records this season and the Raiders are the only ones who appear to be trending in the right direction.
It's pretty much a guarantee that the NFL returns to LA in 2016 so all we can do now is wait to see which team(s) it will be and watch the next 10 years to see how popular and successful it is.