As you already have the case, so your own measurement for the graphics card clearance should be more accurate than the number (240mm) given by Lian Li's website.
For a reference HD6870, the length is slightly more than 248mm which is from the outside of the card's PCI slot bracket to the end of the shroud (with PCIE connectors on the top side). I think this will not fit into Lian Li PC-Q11A due to its length.
Perhaps the best bet for fitting a HD6850 is to get the shortest (ie XFX's version) which is 8.66'' / 220mm long.
For 90 degree right angle PCIE connectors, see if this fits your needs:-