The Washington Gas Light Co. applied yesterday for permission to raise its rates for natural gas sold to District of Columbia customers by 11.8 percent.

If approved by the D.C. Public Service Commission, it would increase the average monthly bill by $7.50 for customers who heat their homes with gas. For those who cook with gas and make only other incidental use of the fuel, the average increase would be $2.81. The current average bill the year round for heating customers is $63.01; for others, it is $23.46. Brian Lederer, the D.C. people's counsel, who by law represents the public interests before the PSC, said after scanning the company's application that it contained extraordinary request "that we will litigate very vigorously." He said the company is proposing to increase the return on its stockholders' equity from 13 1/4 to 18 percent.

In the announcement of its application, the company said it needed the additional revenue -- a total of $18.8 million a year -- to meet increased wages and other operating costs, an expanded construction program and the rising cost of captial, including higher interest on borrowed funds. On Thursday, the PSC authorized Washington Gas to borrow $30 million at a maximum annual interest rate of 16 1/4 percent -- more than twice the 7 1/2 average rate the company is now paying on borrowed money.

The increases would apply to 148,000 residential and commerical customers in the District. The company has not requested increases for customers in Maryland or Virginia, but Paul Young, its manager of news media relations, said he expected such applications would be filed later this year.

Given the time needed for public hearings and deliberations by the PSC, Young estimated that any District increase could not go into effect until early 1982.