There are basically two mechanics that will heal the boss during this fight. Beside them, regular Fire Damage also heal it, but you shouldn't be using it at all.
1. The Organic Matter
The Baron from Below will heal to full health if you don't kill the Organic Matter in 8-10 seconds (I'm not sure which one to be honest). If it was always healing it means your team lacked the necessary DPS. You can easily tell by the orange message that appears in the room, which will either be that the Baron consumed the Organic Matter or that you destroyed it just in time.
Killing this boss with 8 players is possible, but they need to be reasonably high (I'd say at least 600 on average, maybe more), and of course, everyone must be doing full damage on the Organic Matter. If your team isn't that strong, I suggest getting 2-3 extra players to make sure you have the damage required.
2. Aggressive Lava
The Aggressive Lava also has a mechanic that makes the boss heal. It's not exactly that all their attacks heal the Baron, or you'd see it happening more often, but if they stay alive the boss too long, it will heal a lot more. To prevent that, you must be either killing them very fast or have some players off tank them with some distance. Since they spawn in different places around the room, you'll probably end up doing both. But make sure they don't stay alive near the boss for too long, since it will also make the fight take longer.
This is easier to notice with a smaller team like yours too, since the healing will have a bigger impact and the Lava will probably live longer if not dealt with properly.