SELECT 
  MIN(cscart_product_prices.price) as min, 
  MAX(cscart_product_prices.price) as max 
FROM 
  cscart_product_prices 
  LEFT JOIN cscart_products as products ON products.product_id = cscart_product_prices.product_id 
  LEFT JOIN cscart_product_prices as prices_2 ON cscart_product_prices.product_id = prices_2.product_id 
  AND cscart_product_prices.price > prices_2.price 
  AND prices_2.lower_limit = 1 
  AND prices_2.usergroup_id IN (0) 
  INNER JOIN cscart_products ON products.product_id = cscart_products.product_id 
WHERE 
  products.status IN ('A') 
  AND products.product_id IN ('635129', '635130') 
  AND cscart_product_prices.lower_limit = 1 
  AND cscart_product_prices.usergroup_id IN (0) 
  AND prices_2.price IS NULL

Query time 0.00089

JSON explain

{
  "query_block": {
    "select_id": 1,
    "table": {
      "table_name": "products",
      "access_type": "range",
      "possible_keys": ["PRIMARY", "status"],
      "key": "status",
      "key_length": "6",
      "used_key_parts": ["status", "product_id"],
      "rows": 2,
      "filtered": 100,
      "attached_condition": "products.`status` = 'A' and products.product_id in ('635129','635130')",
      "using_index": true
    },
    "table": {
      "table_name": "cscart_products",
      "access_type": "eq_ref",
      "possible_keys": ["PRIMARY"],
      "key": "PRIMARY",
      "key_length": "3",
      "used_key_parts": ["product_id"],
      "ref": ["staging2_wesave_com.products.product_id"],
      "rows": 1,
      "filtered": 100,
      "using_index": true
    },
    "table": {
      "table_name": "cscart_product_prices",
      "access_type": "eq_ref",
      "possible_keys": ["usergroup", "product_id", "lower_limit", "usergroup_id"],
      "key": "usergroup",
      "key_length": "9",
      "used_key_parts": ["product_id", "usergroup_id", "lower_limit"],
      "ref": ["staging2_wesave_com.products.product_id", "const", "const"],
      "rows": 1,
      "filtered": 100
    },
    "table": {
      "table_name": "prices_2",
      "access_type": "eq_ref",
      "possible_keys": ["usergroup", "product_id", "lower_limit", "usergroup_id"],
      "key": "usergroup",
      "key_length": "9",
      "used_key_parts": ["product_id", "usergroup_id", "lower_limit"],
      "ref": ["staging2_wesave_com.products.product_id", "const", "const"],
      "rows": 1,
      "filtered": 100,
      "attached_condition": "trigcond(prices_2.price is null) and trigcond(cscart_product_prices.price > prices_2.price)",
      "not_exists": true
    }
  }
}