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Lead acid batteries supply 13.8V when fully charged. Devices nominally rated 12V are usually fine with that. e.g. all the electrical equipment in cars. I'm not an electrician but it appears that once the voltage drops to around 12V under load it needs charging.
What you should be more concerned with is making sure you connect the terminals the right way around. You could go so far as to put a heavy duty rectifier diode in circuit so you can't get it wrong.
You might find you have to use multiple lighter sockets in parallel if you want to run more than one device. They have a limited power rating and a couple of high current devices on a double adapter might exceed that.
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