The actions, which have been described as “deplorable” by police, are believed to have been committed overnight on Wednesday.
The graffiti was discovered on Thursday morning by the manager of Clitheroe Castle Museum.
A paint pot lid, paint brush packaging and a receipt for Hammerite paint was found close to the scene on Castlegate at around noon by a Clitheroe PCSO.
Sgt Dave Simpson, from Clitheroe Police, described the vandalism as “deplorable” and “disrespectful”.
Community stalwart Mel Diack MBE, who is well known for his work with Clitheroe Youth Forum to compile a Book of Remembrance of those who lost their lives during the Second World War, said: “It’s deplorable and very sad that this has happened.
“Whoever has done this must have no concept of what a war memorial is and why these brave servicemen have been honoured and are to be remembered. It is a sad reflection on some idiots who have nothing better to do.
“When caught the courts should actually take them to the graves of some of these brave souls who gave their lives for liberty and try and educate them in what it meant to fight for their freedom. I hope that they are caught as soon as possible.”
Robert Thompson, chairman of Ribble Valley Borough Council’s community services committee, said: “We take vandalism to public property, including memorials to our fallen heroes, very seriously and will be taking every step to find the culprits.”
Ribble Valley Borough Council staff have since cleaned the graffiti.