Is this FA really equivalent to the given regular expression? From the picture, the automata can accept $(\text L|\text D)^*$ following say $\_\text L\text D$, but in the formula above $(\text L|\text D)^*$ can't follow the $\_\text L\text D$.

So the Automata in the picture is not equivalent to the RE?
They aren't equivalent. For example, the string "L__L" is described by the expression, but not accepted by the automaton (no way to have two '_' in a row).