Part of the nested lists

You could "transpose" your lst using Flatten (1), and then take the 4 element:

Flatten[lst, {{2}, {1}}][[4]]

{d, h}

1. Flatten command: matrix as second argument

Cases[lst, {_, _, _, x_, ___} :> x]

{d, h}

Here's another approach using Query that's perhaps a bit more explicit about what's happening:

Query[DeleteMissing@#&, 4]@lst

The slightly strange @#& part is there to "hide" DeleteMissing from query to make sure it's applied after the selector 4. (In "Query language": we make the typically descending operator DeleteMissing ascending)