The start of the D.C. lottery's new $100 million-a-year daily numbers game may be delayed even further because of the nationwide telephone strike, a top official of the company hired to run the game said yesterday.

"The telephone strike . . . does create a problem," said P. Leonard Manning, the chief executive officer of Lottery Technology Enterprises.

Manning said telephone lines are a vital link in the computer-based daily numbers game system, which is now being installed in businesses throughout the city.

Each business licensed to sell daily numbers tickets will use a computer terminal to produce the tickets, and phone lines must be installed to hook up individual terminals to a central computer.

As the strike completed its third day yesterday, the Chesapeake & Potomac Telephone Co. was continuing to rely on between 2,500 and 3,000 management and supervisory employes to fill in for 11,500 union employes in the Washington area.

Company spokesmen have said C&P will perform installations and repairs but pointed ouit that priority is being given to emergency situations such as loss of phone service by hospitals, fire and police departments and other essential government agencies.

Douglas Pompey, a C&P accounts executive who oversees the D.C. government's phone system, said there undoubtedly will be some delay in installing the daily numbers system because of the strike. Pompey said that some management employes worked on installing equipment for the daily numbers game yesterday, but "the lottery board takes no higher priority than any other service."

Lottery board chairman Brant Coopersmith said yesterday that "any slowdown or delay will cost us revenue, there's no question about that."

The lottery's instant game, which has been in operation since last August, already has provided the city with about $16 million in revenue through July 31, according to lottery board controller George Thomas.

Lottery revenue for the 1984 fiscal year, which begins Oct. 1, is expected to rise to $40 million, with the more lucrative daily numbers game supplying about $28 million of that amount.

In the current fiscal year, the city, which is seeking to come up with $14 million in savings or additional revenue to balance the budget, already has lost several million dollars in estimated revenues because of a controversy over the lottery board's decision to award the daily numbers contract to Manning's firm--a dispute that forced the board to postpone the game that was scheduled to start July 18.

When the contract finally was awarded to LTE in June, the start-up date was changed to Oct. 15. Lottery and LTE officials recently had expressed hope that the game could begin by late August or early September.

Before the strike, Mayor Marion Barry last week called C&P vice president Delano Lewis, who is in charge of C&P's Washington operations and a Barry supporter.

Barry asked if the telephone company could install the daily numbers' phone lines faster, according to Annette Samuels, Barry's press secretary.

Manning said he appreciates the mayor's help and believes it led to C&P's decision to send out installers to work on the game last Saturday. But the strike has now left the firm's chances of beginning the new game early in doubt, he said.