Within the next three years, computer crime training should become standard for all police recruits and investigating computer crime should be a routine matter for local police stations, she said.
Lemon, who will take over responsibility for merging the unit into the newly formed Serious Organised Crime Agency, plans to drive through improvements in the way local forces handle and investigate computer crime.
"I heard one report of a customer who had gone into the local police station to report a crime on eBay. The officer did not know what eBay was. It is just not acceptable," she said.
"I am not suggesting every officer should be an expert, but there should be a clear map for people wanting to report computer crime."
In an interview with Computer Weekly on her second day in the job, Lemon highlighted her determination to raise the confidence of businesses in reporting crimes to their local police high-tech crime units.
By next year, she hopes to oversee the creation of satellite offices that will act as a resource to local police forces investigating computer crime.
"Part of my role is setting standards for home forces, providing good practice and setting up an inspection regime against those standards. So if a member of the public or a business reports a high-tech crime, they know they are going to get a minimum standard of service," she said.
Lemon said her previous experience, which includes head of the National Crime Squad's Firearms Unit and, more recently, head of the Paedophile Online Investigation Team, will help her to bring "traditional policing" values into high-tech crime.
Encouraging software and hardware suppliers to design out computer crime - a technique used in the motor industry - will be a priority.
"If you buy a car now you expect a locking device. You expect anti-theft systems and seat belts. Those traditional designing out methods can be applied to the high-tech arena," she said.
Raising the public's awareness about computer crime through government initiatives such as operation Endeavour will create a demand that will put financial pressure on suppliers to improve security, Lemon believes.
She is keen to quash suggestions that her arrival from the paedophile unit signals a change in direction for the unit.
The government's announcement of a new internet agency dedicated to child abuse is likely to free up more of the unit's resources for investigations into hacking and fraud, she said.
"I think ID theft is probably the biggest worry. It is absolutely massive. It makes people feel vulnerable and that is bad for businesses," she said. "We need to raise standards in the home forces so they have the trust and confidence of business."