Is your monitor calibrated and profiled with a hardware device? If not, all bets are off - it's always going to be a bit hit and miss as to how prints look compared to any particular program. However, if you're not using colour management (with printer profiles) then here's one thing that may make Lightroom print more like Epson software. When you print in LR, in the "Print Job" settings (bottom right of print module), try setting (in Color Management) the profile to sRGB (probably sRGB IEC61966-2.1). First time, you'll probably have to choose "Other..." and find sRGB from a long list.
By default, LR sends images to the printer in ProPhoto colour space, and non-managed printer driver software often won't cope (resulting in dark desaturated prints). Force LR to send the image in sRGB and it's more likely to be about right.