You don't have a pot in the LGPS. That's probably where your calculations are going wrong.
The LGPS is a defined benefit scheme, which works in a completely different way. The amounts you and your employer pay in are irrelevant to the size of pension you get - it is calculated on length of service and salary.
And that 'stupidly small amount' is paid for the rest of your life - it's not a 'piggy bank' style pot of money that can run out like the OP's pension. That's why it looks small if you compare it with a defined contribution pot.
The amount you put in depends on your salary, so the calculation below is just an example and you may need to adjust the input percentage. But let's assume your salary is £40,000.
You pay in 6.5% = £2,600 a year.
You accrue 1/49 salary a year = £816.32.
That does look a lot less than you paid in.
But if you work there for 20 years that's an annual pension of £16,326.
The amount you've paid in over 20 years is £52,000.
Still a lot more than you're getting back? Remember it is paid every year.
So after 3.2 years of drawing your pension you have got back as much as you paid in. And they keep paying. You have a life expectancy of around 12 years after retirement, so another 9 years or so of pension.