'Live and let live' is a much busied normative saying. That the saying is normative means that it norms. This in contrast with descriptive sayings which are describing (for instance: 'the apple doesn't fall far from the tree'). With the use of the saying 'live and let live' others are incentivized to take a certain attitude. This attitude consists of the two parts of 'live' and 'let live'. With the use of the word 'live' is the one to whom the saying is directed incentivized to act as he chooses. And with the use of the words 'let live' is the one to whom the saying is directed incentivized to let others act as they choose.
The saying is often directed to someone who complains against another that with his acting he causes him hinder. The complainer is thereby incentivized to let the other free in his acting, and act himself as he chooses. With the use of the regarded saying in this contexts it must however be considered that 'life' in that saying does not necessarily include the causing of hinder, while 'let live' in that saying does necessarily exclude the causing of hinder. When you act according to your own choice this does not necessarily mean that you are hindering another with that. But when you let another act according to his own choice, it is necessary that you are not hindering the other therein. The saying 'live and let live' says actually 'act according to choice without hindering' or 'act unhindered hinderlessly'.