Lose - Be deprived of/cease to have
The first two sentence are fine [nb, space after a comma], except that to be fluent you will not repeat "hand". You will use "it". If you split the sentence into two sentences with a full stop, then "hand" can be repeated.
The last sentence is not acceptable. You could rephrase it as "You may have to lose your hand [it will have to be cut off] if you put it in the automatic doors.