Lesser Relics are consumable items that can only be found within the Ancient Relics gamemode. They provide an interval reduction for the respective skill along with a secondary modifier (usually combat related). They can be acquired in Non-Combat Skills (excluding Farming, Township, Alt. Magic, Cartography, Archaeology) at a rate of 1/1,000 (0.1%) per action and will always drop 300 at a time. You will not get Lesser Relicss for any other skill than the one you are current training.
Lesser Relics are considered a "Global Rare Item" and thus benefit from Clue Chasers Insignia, Ghostly Parrot, Woodcutting Ancient Relic 5, and any other source that increases Global Rare items.