You can buy lockpicks in Oblivion primarily from the following sources:

• Shady Sam : He is the most accessible vendor early in the game, located outside the Imperial City walls near the Chestnut Handy Stables. Shady Sam sells lockpicks at 6 gold each and stocks up to 30 lockpicks daily. His inventory refreshes every day, allowing you to buy more if you run out

• Thieves Guild Fences : Once you join the Thieves Guild, you gain access to fences who sell lockpicks in larger quantities, usually up to 100 lockpicks per vendor. The first fence you encounter is Ongar the World-Weary in Bruma. Fences sell lockpicks at a similar or slightly better price than Shady Sam, but you must be a guild member to buy from them

• Looting : You can also find lockpicks by looting bandits, goblins, and chests in dungeons and caves, especially goblin caves. This method requires combat or exploration but is a free way to stock up on lockpicks

In summary, for buying lockpicks without joining any faction, Shady Sam is the best and most reliable vendor. For larger quantities and better prices, joining the Thieves Guild and buying from fences is ideal. Additionally, looting remains a consistent way to acquire lockpicks without spending gold