I have not used Laptop Lane myself but I have noticed that there are 2 in Terminal 1 (sounds like you're flying UA). One is in Concourse B down by gate B5 (IIRC) and the other is in the connecting tunnel between concourse B & C, under the escalators to B & close to the escalators to baggage claim. I would figure there's a charge for access but they have their own desktop PCs there so you wouldn't have to worry about equipment. Not sure what their policy & requirements are for using your own laptop though. HTH...
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Regards,
- Anna