If I choose off-blockchain transaction in
Lightning network is it any mechanism to check wether balance covers mount of transaction? So is it, or isn't it possible spend two times the same amount of balance?
The lightning network consists of many payment channels between users on the network. Each channel has a certain amount of bitcoin locked up in it, and that amount is the maximum which can be transferred in the channel, you cannot add any more BTC. So it is not possible to spend double the balance, no.