The local government pension scheme is a "defined benefit" scheme, with the final pension being based on your earnings in each year of service (after 2014), with the benefit being "index linked" so it keeps up with inflation. For each year of service, you'll get a pension of 1/49th of your salary for that year, uprated for inflation ("Cost of Living").
Although a bit less generous than a "final salary" scheme where the final pension would be based on your final salary with the employer, these are still generally considered to be very good pensions and much better than "defined contribution" schemes where your pension ends up dependent on investment returns.
As a member of the LGPS, a substantial part of your pension will be funded directly by your employer: their contribution varies, but is typically 2/3rds of the cost. If you instead contributed to a private pension, you wouldn't get that employer contribution, so you'd need some really amazing returns to beat the LGPS pension.
You mention wanting to retire at age 55. The LGPS does allow you to take early retirement. Currently this is stated as being from age 55 in exchange for them reducing your pension because it'd be in payment for more years.
However, it's quite likely that by the time you retire, the minimum age will have gone up, as the government limit the minimum age you can draw benefits from any pension scheme to 10 years before the state pension age. As you're 30 now, your state pension age is currently expected to be 68 and so your minimum pension age will probably be 58. This will apply to any pension scheme, not just the LGPS.
Another answer mentions it's backed by the UK government. I can't find any specific evidence of this online, though the website does say that the Treasury has input into the cost of the scheme which may imply that they are backing it.
That said, even if it is the case, public sector pensions are a very large unreported liability of the government, and I think that if there were a really major crisis the government might choose to partially default on those obligations and reduce public sector pensions. Although the government can print money, there's a limit to how much they could do this in practice without wrecking the rest of the economy. But if we were in that kind of scenario, your private pension would also probably be in a lot of doubt, whether from the stock market collapsing or from government confiscation.
Overall, the LGPS is the clear winner given the employer contribution and the guaranteed pension, and I think you'd need a really good reason not join it.
