I'm surprised that no BLD solvers posted that they solve the entire cube with "1-look".
So besides that "trivial" answer...
If you define 1LLL as executing a single algorithm on a cube in which its first two layers are solved but its last layer is scrambled to:
A) mess up the first 2 layers
B) restore the first 2 layers and solve the last layer (without first making the last layer more solved for which then you would need to apply one or more algorithms to repeat the process until the last layer is completely solved), then it is possible in two ways:
Assuming you do not solve the first two layers in any special fashion:
1) You memorize 1211 algorithms and what specific case they apply to.
2) You use my (unpublished) mathematical human method. (Technically, my method is 1-look entire nxnxn cube/minx^n).
However, as others have said about option #1, it's probably not going to be that much faster (if at all) than doing speed optimized OLL and PLL.
I'm still trying to find a "smart" way to make option 2 a reality, but the disadvantage of using it is that it's pretty slow (not speedsolving material).
In short, we've pretty got the best speedsolving last layer breakdown right now.