Put my two cents worth in.
Most of us PINCH the pennies for our displays. I was running a HP laptop, with a busted display. Can't remember specs on it but it was a Pavillion and one of those "Entertainment" jobbies with about 4 gig of ram. Worked great. Some reason....got blue screen of death several times. That scared me since it was right at the end of November when it happened. Had already ran my Halloween show with no issues. Sooooo, because of the season already started....my Christmas light budget already depleted, I bought a cheap Asus, 4gig of ram....maybe a 250gig drive. Had Win 8.1 (yuck) on it. It was probably just over $200.00 on Amazon. Worked (works) great. Now, that being said... I won't use that computer as my every day computer. I will also keep my sequences from the previous years on another portable drive (backup, backup, backup!). I do use Dropbox and treat it the same way. I keep the "Show Computer" locked down as far as internet to a certain point. I will open it up to grab a new sequence then shut it back. I will do any updates (Windows) at the first of the season and then allow no more until after. Just so that things do not get changed out on LOR. Most of the time I will use a usb thumb drive to move things from my sequencing computer and show computer....but also keep it on Dropbox and an external as well.
Before this, I did run my LOR show on a older Dell xp machine. If your running a basic show, it MIGHT run ok for some time. It just really depends on what LOR does with the software. Of course as stated before the EOL is coming soon for XP. So I wouldn't put it on the internet after that if you do go in that direction.
Again also if your wanting to go cheap.... you might find some i5 THIRD generation laptops (even refurbed) that would SCREAM on LOR and probably anything else you want to do. Cheaper because of the refurb and the FORTH gen i5 chips are out there.
I would look for something with higher memory. Yeah....my old machine would not handle what I do now. But a very basic LOR show....maybe so.