SIX WEEKS HAVE PASSED since the fire that killed 10 women at the Lamont Street boarding home that lacked fire doors and fire escapes. How has the city government reacted to this tragedy? What has been done to ensure that the 300 to 400 other group homes in the city are safe-and will be properly run from now on?

So far, the Barry administration has responded well. A small army of inspectors from the fire, human resources, environmental and housing departments has checked the 27 group homes owned by the city and the 50 privately owned foster-care facilities operating under contracts with the city or St. Elizabeths Hospital. The inspections, the first that some facilities had received, turned up a raft of violations. Fifteen multistory buildings had no fire escapes. Others lacked smoke detectors, working extinguishers, fire doors or internal alarms. More than one-third had unsanitary kitchens.

Those homes are being reinspected this week. According to Chief Inspector Ralph E. Spencer, his teams have found that roughly 90 percent of the violations have been fixed. The big exception involves fire escapes. Because there is a sudden boom in local demand for fire escapes, some installations may be delayed. Other homes are still trying to find the necessary funds. In these cases, people living on unsafe upper floors have been relocated and their rooms closed. Meanwhile, the inspection teams are moving on to the roughly 280 nursing homes and boarding houses that are privately owned and financed. Most of these are small. Many lack proper licenses. All will get a good going-over, too.

City officials seem determined to make this more than a short-lived flurry of concern. To overcome the fragmentation of local health and safety codes, Mayor Barry is assembling a permanent force of eight inspectors to check every group facility four or five times a year for compliance with all the rules. The city has also asked Congress, again, for money to carry out the 1977 ordinance empowering the Department of Human Resources to regulate all group homes.

Meanwhile, several city and federal agencies are investigting alleged violations of safety, licensing and labor laws by the Volunteers of America, the charitable group that ran the Lamont Street home.

Obviously, the governmental breakdowns revealed by the Lamont Street fire cannot be permanently repaired in six weeks. A large backlog of applications for building-occupancy permits must still be cleared away. The biggest job, overhauling the human resources department, has barely been begun. But the city is moving firmly to ensure basic protections for the aged, ill and otherwise dependent people living in group homes. Moreover, Mayor Barry has sent an unmistable message to every city employee by reprimanding DHR Director Albert P. Russo for failing to carry out the 1977 law, and by suspending, demoting and transferring the building inspector who failed to spot violations at Lamont Street. Maintaining the new forcefulness won't be easy. But it has to be done.