Lee faces a fortnight out while Jones could be missing for up to a month. Sam Lynch (hamstring) is also unavailable.
York lost 28-10 against Sheffield Eagles last week, and Woods admitted: “We didn’t do ourselves any favours.”
He added: “We coughed up easy ball and turned it over at vital stages. We can’t afford to do that this year with the quality of teams that are in the Co-operative Championship.
“You need to be on your game in every game, because you’ll get punished if you’re not.”
Raiders are hoping to claim a first win under the leadership of new coach Nigel Wright.
Woods said: “It’s not a great time for us to be getting them, but we’ve got to worry about ourselves and make sure we get everything done that we want to do.”
Nathan Mossop could make a surprise return for Barrow, despite suffering a shoulder injury against Leigh last week.
But prop Jamie Thackray faces four to six weeks out with ankle ligament damage.