Marination is a culinary term, meaning that ingredients are left to soak in a mixture of flavour enhancing agents prior to cooking. The speaker is trying for a humorous metaphor, to the effect that he or she is going to lie about and rest in the sun in the same way that the beef being marinated will lie around in the soy sauce etc. But the metaphor is not sufficiently natural that it will ever catch on among native speakers. It is notoriously difficult to make a joke in a language that is not your mother tongue, and I can personally attest to that, having had numerous failures.
