Lawyers for the Community for Creative Non-Violence filed suit yesterday to force the Reagan administration to authorize the renovation of a downtown Washington shelter for the homeless or assume operation of the squalid facility.

The suit was filed hours after CCNV members Mitch Snyder and Carol Fennelly were arrested for the second time in four days during a sit-in on the sidewalk outside the White House. Snyder and Fennelly, who were released by a federal magistrate, were charged with erecting an illegal structure and placing private property -- two chairs -- on the sidewalk.

The lawsuit, filed in U.S. District Court in Washington, is the latest development in the increasingly bitter schism between the federal government, which last fall pledged to turn the shelter into a model one, and CCNV, which operates the 800-bed facility at 425 Second Street NW.

Last week, officials at the Department of Health and Human Services rescinded an agreement with Snyder and said they were considering giving $2.7 million in renovation money to the District government for alternative housing.

Snyder, who earlier had accused federal officials of "wasting his time" and reneging on assurances he received last November from President Reagan, took his protest to the White House and said he planned to wait to meet with the president.

Officials in the U.S. Attorney's Office and HHS declined to comment on the suit, which asks a judge to order that a private contractor, not GSA, renovate the decaying, rat-infested shelter using plans drawn up by Snyder's New York architect.

In her 17-page complaint, CCNV attorney Florence Roisman alleges that GSA's plans for the shelter are "egregiously inadequate," in part because they would have men and women use the same entrance, which CCNV argues would endanger women residents. The suit contends that GSA should be barred from making the renovations because it has, in Roisman's words, "demonstrated incompetence, dilatoriness and unreliability in its work at the shelter."

Tomorrow, another team of CCNV attorneys is to appear before U.S. District Judge Louis Oberdorfer in connection with the White House sit-ins. CCNV's lawyers filed suit yesterday asking Oberdorfer to issue a temporary restraining order that would bar the government from arresting those who sit in chairs while conducting vigils outside the White House.

Officials in the U.S. Attorney's Office say that the folding chairs violate security regulations. CCNV's lawyers claim that such an interpretation is unlawful because it would bar handicapped people in wheelchairs from exercising their constitutional rights of free speech and assembly.