SELECT 
  cscart_product_prices.product_id, 
  MIN(
    IF(
      cscart_product_prices.percentage_discount = 0, 
      cscart_product_prices.price, 
      cscart_product_prices.price - (
        cscart_product_prices.price * cscart_product_prices.percentage_discount
      )/ 100
    )
  ) AS price 
FROM 
  cscart_product_prices 
WHERE 
  cscart_product_prices.product_id IN (
    111835, 111837, 404082, 406110, 429201, 
    431252
  ) 
  AND cscart_product_prices.lower_limit = 1 
  AND cscart_product_prices.usergroup_id IN (0, 1) 
GROUP BY 
  cscart_product_prices.product_id

Query time 0.00036

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost": 0.025467049,
    "nested_loop": [
      {
        "table": {
          "table_name": "cscart_product_prices",
          "access_type": "range",
          "possible_keys": [
            "usergroup",
            "product_id",
            "lower_limit",
            "usergroup_id"
          ],
          "key": "usergroup",
          "key_length": "9",
          "used_key_parts": ["product_id", "usergroup_id", "lower_limit"],
          "loops": 1,
          "rows": 12,
          "cost": 0.0216566,
          "filtered": 50,
          "attached_condition": "cscart_product_prices.lower_limit = 1 and cscart_product_prices.product_id in (111835,111837,404082,406110,429201,431252) and cscart_product_prices.usergroup_id in (0,1)"
        }
      }
    ]
  }
}