While there are not render farms directly supporting LuxCoreRender and no tool to directly support cloud rendering (with AWS, Azure, etc.), some of the many tools supporting Blender rendering on cloud providers (again like AWS, Azure, etc.) are likely to work if they support custom Blender builds (i.e Blender + BlendLuxCore). I was looking in https://www.blendermarket.com/products/barista, it does support custom blender builds but it seems to have an explicit selection of the render engine so it may not work.
If someone is looking for a topic to explore requiring only a bit of technical know-how without the need to write software, this may be an interesting topic.