A printing and mailing firm sued Sen. Robert J. Dole (R-Kan.) for $179,000 yesterday, claiming Dole owes the money to pay for money-raising efforts in his concurrent campaigns for his party's presidential nomination and to win reelection to the Senate.

Computer Business Supplies of Washington Inc. claims in the suit that Dole, his presidential campaign committee, two campaign aides and two corporate defendants have breached their contract to pay the firm for its work, done from April to July 1979.

The total amount sought in the suit, filed in U.S. District Court in Alexandria, is $179,335.16.

The Bob Dole for President Committee yesterday put the blame for the unpaid bills on a firm that it said "wrongly incurred" the debts by contracting with Computer Business Supplies "in express violation" of its contract with the campaign committee.

An officer of that firm did not return a reporter's call.

According to the suit, Computer Business Supplies performed such campaign chores as mailing out "Dole-grams," for $2,079.23, mailing fund-raising letters to "major donors" for $12,720, and "Low $ Thank You" letters for $291.47.

The firm also hand-stamped letters, handed out press kits, and sent letters to such specific groups as Jews and veterans, the suit claims.

The suit filed yesterday seeks to attach any Dole campaign funds that have been deposited in the First American Bank of Virginia in Alexandria, according to court papers.

Dole's fundraising efforts have lagged behind his own predictions, according to news reports. He had claimed he would raise $1 million by late last year, but had raised only $517,746, by Sept. 30, 1979, according to federal election Commission figures.

Dole was elected to the Senate from Kansas in 1968, and was reelected in 1974. He has filed papers seeking a third term in office, according to an aide.

Dole was the unsuccessful vice presidential running mate four years ago with then-president Gerald R. Ford.