The solicitor of the National Labor Relations Board acknowledged to two congressional subcommittees yesterday that he had represented clients in a private lawsuit against a labor union while serving as acting director of a Labor Department office that performs audits of unions and oversees a number of their activities.

But Hugh L. Reilly said he saw no conflict of interest because he worked on the lawsuit on his own time, wasn't paid for his work and never did anything that was related to the suit in his capacity as acting director of the Office of Labor-Management Standards Enforcement.

The suit was filed against the Communications Workers of America and was financed by Reilly's former employer, the legal arm of the National Right to Work Committee, a conservative group that opposes compulsory union membership.

Reilly's testimony came at the second hearing called this month to investigate the NLRB's recent decision to strip its independent general counsel of the powers he has held for 28 years and transfer many of those duties to Reilly.

Democratic members of the two subcommittees holding the hearings claim that the power shift was orchestrated by Republican board Chairman Donald L. Dotson to circumvent the general counsel, who was appointed by President Carter and serves a statutory term.

Dotson previously testified that he had not been the one behind the board's May 4 decision to reorganize the agency.

But at yesterday's hearing, Reilly said that Dotson first talked to him about limiting the general counsel's authority in January or February--before Dotson was sworn in as chairman on March 8.

The two other board members who supported the shift, Republicans Howard Jenkins Jr. and Robert Hunter, also testified yesterday that Dotson had approached them about the change about a month before the May meeting.

Don A. Zimmerman, an independent board member appointed by Carter and the only member to vote against the reorganization, testified that Dotson hadn't discussed it with him until the day of the vote.

That testimony and Dotson's reluctance to supply the subcommittees with documents to show that the switch was necessary and had been thoroughly discussed prompted Rep. George Miller (D-Calif.), to accuse Dotson of pushing through "substantial changes based only . . . on some bad experiences that you had while appearing on the other side of these NLRB cases."

Dotson had testified earlier that his experiences as a corporate labor attorney had convinced him that lawyers on the general counsel's staff often engaged in "sleazy" and "high-handed" practices and frequently "misrepresented board decisions."

Reilly and Dotson agreed during testimony yesterday that Labor Secretary Raymond J. Donovan's office was fully aware of Reilly's participation in the suit against the union and didn't object. Dotson said he had talked to Donovan about it.

A Donovan aide had told a reporter previously that the secretary had not discussed the case with Dotson or Reilly. The aide said Donovan had heard about Reilly's participation from an outside source and then asked his staff to look into it.

Dotson said the board is negotiating with General Counsel William A. Lubbers what powers he will retain under the reorganization.