SELECT 
  jmj_product_prices.product_id, 
  COALESCE(
    jmj_master_products_storefront_min_price.price, 
    MIN(
      IF(
        jmj_product_prices.percentage_discount = 0, 
        jmj_product_prices.price, 
        jmj_product_prices.price - (
          jmj_product_prices.price * jmj_product_prices.percentage_discount
        )/ 100
      )
    )
  ) AS price 
FROM 
  jmj_product_prices 
  LEFT JOIN jmj_master_products_storefront_min_price ON jmj_master_products_storefront_min_price.product_id = jmj_product_prices.product_id 
  AND jmj_master_products_storefront_min_price.storefront_id = 1 
WHERE 
  jmj_product_prices.product_id IN (
    1705, 1713, 1702, 1719, 1723, 1696, 1699, 
    1707, 1697, 1735, 1695, 1686
  ) 
  AND jmj_product_prices.lower_limit = 1 
  AND jmj_product_prices.usergroup_id IN (0, 1) 
GROUP BY 
  jmj_product_prices.product_id

Query time 0.00103

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "41.88"
    },
    "grouping_operation": {
      "using_temporary_table": true,
      "using_filesort": true,
      "cost_info": {
        "sort_cost": "3.39"
      },
      "nested_loop": [
        {
          "table": {
            "table_name": "jmj_product_prices",
            "access_type": "range",
            "possible_keys": [
              "usergroup",
              "product_id",
              "lower_limit",
              "usergroup_id"
            ],
            "key": "product_id",
            "used_key_parts": [
              "product_id"
            ],
            "key_length": "3",
            "rows_examined_per_scan": 17,
            "rows_produced_per_join": 3,
            "filtered": "19.94",
            "index_condition": "(`jmj_test`.`jmj_product_prices`.`product_id` in (1705,1713,1702,1719,1723,1696,1699,1707,1697,1735,1695,1686))",
            "cost_info": {
              "read_cost": "35.13",
              "eval_cost": "0.68",
              "prefix_cost": "35.81",
              "data_read_per_join": "81"
            },
            "used_columns": [
              "product_id",
              "price",
              "percentage_discount",
              "lower_limit",
              "usergroup_id"
            ],
            "attached_condition": "((`jmj_test`.`jmj_product_prices`.`lower_limit` = 1) and (`jmj_test`.`jmj_product_prices`.`usergroup_id` in (0,1)))"
          }
        },
        {
          "table": {
            "table_name": "jmj_master_products_storefront_min_price",
            "access_type": "ALL",
            "possible_keys": [
              "PRIMARY"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 3,
            "filtered": "100.00",
            "using_join_buffer": "Block Nested Loop",
            "cost_info": {
              "read_cost": "2.00",
              "eval_cost": "0.68",
              "prefix_cost": "38.49",
              "data_read_per_join": "54"
            },
            "used_columns": [
              "storefront_id",
              "product_id",
              "price"
            ],
            "attached_condition": "<if>(is_not_null_compl(jmj_master_products_storefront_min_price), ((`jmj_test`.`jmj_master_products_storefront_min_price`.`storefront_id` = 1) and (`jmj_test`.`jmj_master_products_storefront_min_price`.`product_id` = `jmj_test`.`jmj_product_prices`.`product_id`)), true)"
          }
        }
      ]
    }
  }
}