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 (
    5558, 4470, 1906, 780, 2230, 4453, 4457, 
    656, 725, 727, 670, 667, 681, 690, 654, 
    705, 682
  ) 
  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 0.00041

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "40.81"
    },
    "grouping_operation": {
      "using_filesort": false,
      "table": {
        "table_name": "cscart_product_prices",
        "access_type": "range",
        "possible_keys": [
          "membership",
          "product_id",
          "lower_limit",
          "membership_id"
        ],
        "key": "product_id",
        "used_key_parts": [
          "product_id"
        ],
        "key_length": "3",
        "rows_examined_per_scan": 17,
        "rows_produced_per_join": 3,
        "filtered": "19.99",
        "index_condition": "(`ea201_francemaqu`.`cscart_product_prices`.`product_id` in (5558,4470,1906,780,2230,4453,4457,656,725,727,670,667,681,690,654,705,682))",
        "cost_info": {
          "read_cost": "40.13",
          "eval_cost": "0.68",
          "prefix_cost": "40.81",
          "data_read_per_join": "81"
        },
        "used_columns": [
          "product_id",
          "price",
          "lower_limit",
          "usergroup_id",
          "percentage_discount"
        ],
        "attached_condition": "((`ea201_francemaqu`.`cscart_product_prices`.`lower_limit` = 1) and (`ea201_francemaqu`.`cscart_product_prices`.`usergroup_id` in (0,1)))"
      }
    }
  }
}

Result

product_id price
654 2.30000000
656 2.30000000
667 2.30000000
670 2.30000000
681 2.30000000
682 2.30000000
690 2.30000000
705 2.30000000
725 2.30000000
727 2.30000000
780 4.95000000
1906 13.35000000
2230 7.95000000
4453 13.00000000
4457 13.00000000
4470 7.25000000
5558 26.15000000