The Federal Aviation Administration will start lifting in July some of the air-traffic restrictions imposed last August when air traffic controllers went on strike and were fired, FAA Administrator J. Lynn Helms said yesterday.

Helms told the Aero Club yesterday that the agency will lift restrictions first on flights that pass through the region controlled by the Salt Lake City en route center, one of 20 FAA centers that control air traffic between airports.

The change would allow airlines and private pilots to land and take off at airports freely within that area--the better part of five states--without arranging ahead for permission for the aircraft to pass through the area.

Flights operating from the Salt Lake City area through still-controlled areas would remain constrained and would continue to require the necessary FAA operating rights--called slots.

The lifting of controls at Salt Lake City will be followed by similar action at the Seattle center in August and the Albuquerque center in September, Helms said. Controls at the other 17 regional centers would be lifted one by one, he added. It was not clear when restrictions on the Washington region would be lifted.

"We're going to take the restrictions off center by center across the country, instead of trying to absorb it all at once," Helms said later.

Helms noted that the release of contraints is being made without a single new controller yet on board, but solely as a result of increased efficiency and productivity. The first class of newly trained controllers will begin working as operational controllers in late August, with the numbers coming on board increasing with successive months, he said.

The centers picked for decontrol first also reflect the fact that some areas of the nation--like the West--were affected less seriously by controller walkouts than centers in the East and Midwest.

Although the plan to lift air traffic controls was welcomed by airline representatives, some indicated that the most serious operational problems are at centers and airports whose restraints are not scheduled to be lifted until spring and summer of 1983. They include Dallas/Fort Worth, Houston, Chicago, Minneapolis and New York.

Helms said that the system nationwide is now operating at 83 percent of its pre-strike capacity and will grow to 90 percent in September. By the end of April 1983, he said the system will be at 100 percent of its pre-strike capacity, but with some restrictions on demand for arrivals during peak hours. By the end of 1983, there will be no remaining restrictions, he said.

Although Helms and other FAA officials have said before that the agency doesn't like being in the slot allocation business, aviation industry officials repeatedly have expressed concern that FAA might use its current "flow-control" mechanisms to continue to regulate the airlines' movements system indefinitely. Some have charged that the FAA may like its its new-found power to control the airlines, and that it may seek to avoid staffing up to pre-strike levels by continuing to control traffic--smoothing it out hour by hour--so that there are no "peaks" in flights that require extra personnel at some hours.