If you're flying a SID through a very busy TMA why should there be ANY delay in executing a "DIR TO"? When I'm given a DT I do it immediately, probably within 2 - 5 seconds.
How did this aircraft head off in the wrong direction for 10 miles!? Were the crew doing the crossword or finishing their breakfast? I know I wasn't there etc etc ...... but this is very worrying. As RD points out, what if LAM had been a bit more full?
If you can't find the waypoint (possibly because you've "tidied up" the departure in the FMS

) just ask the controller to spell it! Delving into a chart whilst plundering straight on in the TMA defies belief.
Out of interest is DIDGO on an FIR boundary? I always underline the boundary waypoints on the plog as it's highly likely that long directs will be to the boundary of the FIR - saves seaching rapidly for the point and gives a good "heads up".
A4
PS The newer busses give the option to "undo" a direct to if you get a bit of finger truoble.