Transport Secretary Grant Shapps launched national campaign has been launched offering cut price journeys around the country.
Mr Menzies hopes the promotion will help even more people visit Fylde during what should be a bumper Fylde.
Mr Menzies said: “With families facing rising bills this is a welcome boost and means many more people should be able to enjoy a day out, whether in our rural towns or by the seaside.
“With cheap fares available from Manchester, Liverpool and places like Blackburn to Preston and onwards to Fylde this will make travel affordable for lots of visitors.
“It is great to see that people are being encouraged to use public transport to explore what Lancashire and Fylde has to offer.”
While Mr Menzies welcomes the Great British Rail sale, he is frustrated those travelling from places like Manchester to some destinations in Fylde will only benefit if they buy two separate tickets.
He said: “The discounts people can achieve are great but because people have to change to reach Lytham and St Annes the process is more complicated.
“I would encourage Northern to consider how cheaper fares can be delivered on more journeys, ensuring Fylde benefits just as much as places like Blackpool.”
Northern Rail, which serves Fylde and the greater Lancashire area’s stations, is offering £1.50 advance purchase tickets up to May 27, but has warned “once they’re gone, they’re gone”.