Virginia Attorney General Anthony F. Troy issued an opinion today that backs the eligibility of Charles S. Robb to run for lieutenant governor.

Questions have been raised about Robb's eligibility because of a provision in the Virginia Constitution requiring lieutenant governors to have been registered voters for the five years before being elected to office.

For the first 10 months of the five years preceding the state election next Nov. 8, Robb was listed on Arlington County voter registration rolls but was ineligible to vote there because he did not have a place to live in the county. When he sold his home in Arlington in 1972, he did not transfer his registration to Albemarle County, where he then lived, and was not again registered at his place of residence until Sept. 28, 1973, in Richmond.

However, in a letter to state Democratic Party Chairman Joseph T. Fitzpartrick, Troy said he does not think it is necessary to be eligible to cast a ballot in order to be a registered voter. "I am of the opinion that a registered voter is a person whose name appea's on the voter registraton records of the Commonwealth of Virginia," he said.

He said the attorney general's office said in a 1971 opinion that a registered voter is not necessarily a qualified voter.

Fitzpatrick must certify candidates in the June 14 Democratic primary to the State Board of Elections by April 20.