Lawes was forced off in the 15th minute of the Challenge Cup last-16 clash, which Saints lost 31-21.
And when asked for an update on the lock at Tuesday's media session, Boyd said: "Courtney had a compound dislocation of his thumb.
"It was quite nasty because the bone actually came out.
"But it's been popped back in, it's been irrigated and sewn back up again.
"He's still got some medical decisions to be made around the skeletal function of the thumb and the muscle and ligament situation.
"All I can really say until we get a clearer medical view is that he won't play on Saturday.
"He came into training this afternoon and he was pretty upbeat.
"He was disappointed and he didn't want to look at it because he knew it was going to be a bit challenging, but he's as good as can be.
"He certainly needs specialist consultation to make a decision on what is the best course of action for him going forward.
"The hand specialist will come back and say 'x, y or z' and whatever he says will happen."
Saints look set to also be without Dan Biggar at Bath on Saturday after the Wales skipper was sent off against Gloucester for a high tackle.
Biggar faces a video disciplinary hearing on Wednesday.
And Boyd said: "It's not helpful when that happens to your two British & Irish Lions.
"They're both pretty important cogs for us.
"Last week we were in pretty good shape squad wise but this week it's been a bit different.
"I've always said in the Premiership is that one of the biggest things for success in this league over a long period of time is keeping your squad healthy.
"We were in a pretty good space a week ago but now we've got those plus a few little niggles this week so the picture has changed."
If Biggar is unable to face Bath, James Grayson and George Furbank will be the main contenders to take over at 10.
"We've certainly got at least two options so we'll pick our way through that this week," Boyd said.
"I suspect both (Grayson and Furbank) will be involved in the game in some shape or form."
Saints were without Fraser Dingwall last weekend as the centre was forced to drop out of the squad at late notice.
But Boyd said: "He hasn't trained this week but he's a possiblity for the weekend."
Saints will definitely be without Courtnall Skosan, who suffered a hamstring injury against London Irish last month.
"He's not ready from the hamstring injury yet," Boyd said. "He's still out."
Karl Wilkins and Tom Wood are also still out.
"They're not ready for this weekend," Boyd said.
"It's knee for Karl and Woody's long-term shoulder is not too far away but he's in a race for time for the end of the season."
But Saints are able to call upon talented youngsters Ollie Sleightholme and Manny Iyogun at Bath.
"Both of them will be available for selection but we've been happy with other guys in that space," Boyd said.
"We've yet to make some decisions but they certainly come into the availability."