It is always advised to not keep your bitcoin in exchanges especially in those exchanges which do not have strong security. I am also using localbitcoin for my trade but I do not transfer my bitcoin to that exchange. I only use that exchange for to search for the high rated buyers and sellers of bitcoin in my own area and then I do contact with them and meet them to exchange my bitcoins. That may be the best way of dealing on localbitcoin exchange.
Besides that if you are keeping some bitcoin for trade then always use good exchanges. I do trade mostly on Bittrex and my money is secured at there. I mostly invest for long term and when I buy some coins then transfer my coins to my desktop wallet.
If you do not use your bitcoin and have to leave them idle then do not leave them on any web wallet or any exchange wallet but keep them in your paper wallet or desktop wallet for increased security.
If you have fund on localbitcoins also no problem for it. First you need to set the 2FA to have the better security for the wallet mate. I use to keep my find LBC but I did not find any of my fund lost in there.
I would like to take the money out to fiat cash means localbitcoins would be right.
Better if you do not know to use the exchange wallet properly you can go to the normal private key secured wallet for it.