What do you actually need to flash a ROM on an LG Stylo? What's the procedure?
If it requires some proprietary device specific tools and drivers that's Windows only, which quite a few phones do, it might be very difficult or impossible to do in Linux. If it's just a question of copying a ROM image zip to a micro-SD, and flashing via the recovery, doing that in Linux should be no problem. Is it a custom ROM or an LG stock ROM?
This guy is using something called LG Flash Tool, which is on Windows, and I presume a Linux version doesn't exist.