Possible ? By spending a ton of money and time developing a webapp similar to LSDS which will parse the .pages, replicate its functionality and render the output? Sure. Why ? I have no idea.
Pretty sure that's the taglib telling you that the files aren't present on the local server. The easy answer is to configure OD to deploy the .page files onto your custom application's server. The hard (and purely theoretical) answer is to override classes internal to the taglib to go resolve those files from elsewhere.