Hi Speedy,
Yes, lying down is more conducive to falling asleep as that is one of the ways the body perceives it is time to sleep. Sitting upright in a comfortable chair, but without the head/neck supported is a good way to be comfortable, but also to get an indication if you start to fall asleep as the dropping of the head will wake you up again.
As for time... well, time is observed when you are focused on something in the material world e.g. the senses or thoughts. Meditating such that time appears to have passed without noticing could be a good indication of being in a deep meditative state, providing you were also in complete awareness at the time. Certainly the lack of awareness of time passing is nothing wrong at all, and our bodies are usually very good at bringing us back to the 'real world'

when our time for meditation is complete, which we can usually simply tell ourselves how long we want to meditate for before we begin; and leave the body clock to do the rest.
Hugs
Giles