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 (
    339, 1565, 1566, 1567, 1568, 1569, 1570, 
    5556
  ) 
  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 0.00043

JSON explain

{
  "query_block": {
    "select_id": 1,
    "table": {
      "table_name": "cscart_product_prices",
      "access_type": "range",
      "possible_keys": ["product_id"],
      "key": "product_id",
      "key_length": "9",
      "used_key_parts": ["product_id", "lower_limit", "usergroup_id"],
      "rows": 16,
      "filtered": 100,
      "index_condition": "cscart_product_prices.lower_limit = 1 and cscart_product_prices.product_id in (339,1565,1566,1567,1568,1569,1570,5556) and cscart_product_prices.usergroup_id in (0,1)"
    }
  }
}

Result

product_id price
339 12.95000000
1565 12.95000000
1566 12.95000000
1567 12.95000000
1568 12.95000000
1569 12.95000000
1570 12.95000000
5556 12.95000000