Would this fit? If not any other cool looking cases with silent external PSUs that this board would fit?
TIA

Probably not. The LC09 is a mini-itx case. The Aopen board is a micro-ATX board.

Here's an intro to Mini-ITX.

I'm personally drooling over the Silverstone LC11B, but I've given thought in the past to some of Coolermaster's offerings, the ATCS line and the Cavalier line.
Lian-Li has a couple offerings in this area that may work (not the PC_9100 though).

I have an Aopen P-M board in a Silverstone LC11 case, and so far I am not too impressed.

Biggest problem is that there is really no space between the lowest slot and the bottom of the case. And of course the lowest slot is used for the AGP card. This means: 1) The Zalman VF-700 VGA cooler won't fit because the back bracket hits the bottom panel of the case. 2) The VGA/DVI connector is too close to case edge that it interferes with plugging in the VGA/DVI cable, unless your cable has a slim metal connector.

All this could have been avoided had Silverstone made the case even a 1/4" taller, or used a riser design that put the AGP card in the middle slot, rather than the bottom.

OTOH, the case certainly looks stunning, and is very quiet.