Personally, I feel in-game it doesn't matter so much. Generally Life Orbs are given to Pokemon more suited to dealing damage (like Incineroar) rather than Pokemon like Sylveon which are better at providing support to the team, and are generally used defensively.
These points are keeping in mind how people play online, so if you need it specifically for in-game, then equipping Sylveon with a Life Orb is not a bad idea, seeing how its moves are all damaging, so they all benefit from it. You should be careful about the recoil damage, and use Potions or moves like Wish to heal up from time to time.
Another suggestion I'd like to make, but off topic, is that having so many Pokemon with their own Z-crystal might be redundant, and might be using up item slots. If you have other items at this point in the game, you should try to equip those instead.