There is a portable version of OpenLP that would allow you to run OpenLP from a USB drive., Once installed to the USB drive you can simply plug it into a suitable computer and you would be up and running. The performance might be a bit slower than from a regular disk drive but it is workable.
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You can also move the location of the OpenLP data Just go to Settings -> Configure OpenLP... and then click on Advanced. The Data Location section shows you where your OpenLP data is located currently and gives you the option to choose an alternative path. You can create a folder on a USB drive and then choose this as the location. When you close OpenLp the data will be copied to the USB drive. Next time you start OpenLP It will use this new location - I haven't tried it but I guess OpenLP will complain bitterly if you start it up without the USB drive.
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Hope this helps,
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-PaulR