i have an old poulan 2-cycle gas trimmer i got from a friend.
first summer i had it the gear in the head stripped so I had to buy a whole new head for $30.
the original was greased and was all brown and dried out.
the new one came with a light colored (lithium?) grease and there was very little. before i even installed it on trimmer i pulled it apart, cleaned it out, and regreased it. Used lucas green polyurea grease because it's what I had on hand but it was too hard and didn't lube that well. Cleaned it and regreased with lucas lucas red n'tacky and that seems to do very good. i've checked the head 2 or 3 times over the past 1.5 years and it's perfect.
any type of equipment like this is always greased very sparingly so i would grease it. i would look for a softer more fluid grease since the gears will be spinning fast.