LaCie drive won't mount is a serious problem that can ruin your data. You just attached your LaCie external hard drive to you Mac system so that you can access some of your important files but it isn't mounting. All the data inside it has become inaccessible and you are also not able to write any new file on it. The fist thing you should check is the connectivity, whether the cable is properly inserted or not. But if still the LaCie drive won't mount then there can be an issue with the hard drive or the Mac OS X itself. You can try to deal it by using the disk utility but if does not prove effective then there can be a case of physical damage. See if the drive has proper power supply , if yes then check if it is giving any beeping or strange noises. If any of it is true then you will have to consult a professional and they will be able to fix LaCie drive won't mount issue. But there are chances that the drive will be formatted and all the data will be lost. Now to recover your lost data you may try to use the LaCie drive recovery software.