There is no set specific time that you need to sit in a lotus position, or any other position, to receive the full benefits of meditation. Some people feel rejuvenated after just a few minutes of meditation while others need to spend more time in order to feel the full benefits for themselves.
I would recommend trying different positions for different lengths of time and comparing how you feel after a meditation session. Once you feel the benefits you are seeking, continue that pattern for as long as it is effective for you.
People often compare meditation to a gym exercise. You do it in a particular way. Yes, it's true that the lotus position during meditation has the most benefits, but it's not the only way to meditate.
The answer depends on why you meditate. If it's for general well being and freshening up the body every morning that you wake up, then the lotus position is perfect. Some people meditate to increase focus and concentration and that aspect of meditation is more important to them than its effect on the body. There are people who meditate reclining, standing, or even walking. Art itself is a form of meditation. Painting is considered as the best alternative to lotus meditation and is even used as a solution for depression in adults who prefer not to meditate the traditional way.