Your problem might be linked to your ignition. Typical parameters are, whether your Spark plug is ok and also the timing of your Ignition. Here a link to an article, where a two-stroke SI engine is compared to an LPG powered engine, maybe it can help you.
I can help you to solve your problem but I need necessary information about your LPG kit. Please send me the scheme of devices connections or photos of devices which are mounted on your engine.
Your engine - one cylinder, SI and two stroke, please explain the lubrification system of this engine.