lolMiner just polls the OpenCL driver and asks for what cards are there and ready 2 run at the moment, nothing more. Its not an own routine, it just uses OpenCL standard functions. That said: I have seen this on my dev rig some time ago too. In the end it turned out to be a riser that somehow did not want as I did. But hard to say what causing this at your side.
AMD Radeo HD 7450
Generally yes, but performance will be rather poor. Also only MNX and Aion will work because of only 1G of memory. So ... I have to admit I can not recommend doing so because unless you have free electricity the sol/s this old card (was low end in 2012!) will not justify turning your computer on for the time your mining.
By the way heavily working on 0.6 ... will take a while till its all done. But hope it will be great