The Noctuary (D&D 3.5e, Level 20+ Adventure)

[Archmage1]

Burning Spear: Sure.

By Mummy, I presume you mean the Mummified Creature template?

That has 4 LA.
So you can buy off the first time when you hit character level 12. This is when your character is ECL 16, and the cost is (ECL-1) * 1000, or 15000 XP. In this game, that would put you at 185000 XP, which still puts you at ECL 19.
At that point, you are a level 12 character with 3 LA, ECL 15.
You will be able to buy off a 2nd LA in(LA*3=9) more class levels, which you will hit at level 21, ECL 24, at which point you can pay 23000 XP to go down to 2 LA.
You would start with a level 16 character with 3 LA, and 185k XP.

The good news is that you don't need to worry about LA buyoff with Sepulchral Thief yet.
You need to hit class level 18 to buy it off, which is ECL 24. We're at ECL 20 currently.(So you would start play with a level 14 sepulchral thief)

In all seriousness, I really wouldn't recommend taking any LA > 4, and I'd think long and hard about whether LA 4 is worth it. It gets increasingly harder and harder to claim that the LA is worth it. At level 20, 3 LA can be fully brought off(Although you will be a couple of levels behind everyone else). At level 30, LA 4 can be fully brought off.