The High Court in Glasgow heard that Ms Spence told Julie Martin, 41, the manager at Aqua Laundrette in Great Western Road, Glasgow, that she needed the clothes by April 14, 2011, as she was going on holiday.
Ms Martin was giving evidence at the trial of Colin Coats, 42, David Parker, 38, Paul Smith, 47, and Philip Wade, 42, who deny abducting, torturing and murdering Ms Spence at a flat at Meadowfoot Road, West Kilbride, between April 14 and 28, 2011.
She told Solicitor General Lesley Thomson, QC, that Ms Spence was a regular customer at the laundrette, but she knew her under one of her aliases, Linda Riley.
Ms Thomson said: "Did you provide the police with information after seeing posters about the disappearance of Lynda Spence," and she replied: "Yes. She came in to get her laundry done every couple of weeks. Every time she came in we would chat."
Ms Martin was shown a laundry ticket in the name of Linda Riley and said the laundry had been left on April 11, 2011.
She added: "She was just her normal happy self. She said she was going on holiday.
"She said she needed her clothes quite soon. I said 'are you going somewhere?' and she said she was going to New York."
The court was told that Ms Spence's laundry bill came to £64.44 and was payable on collection.
Ms Martin said that on previous occasions when Ms Spence paid she would always bring out a "huge amount of cash" and then peel off what she owed.
She was asked by Ms Thomson: "Was the laundry ever collected?" Ms Martin replied: "No."
Under cross-examination Ms Martin revealed that Ms Spence's husband Sokal Zefaj was also a customer at the laundrette.
Earlier the trial heard that Ms Spence emailed private bank Coutts three days before she disappeared, trying to make an appointment in relation to bearer bonds.
Detective Constable Alistair Brown, 50, one of the team of officers from Strathclyde Police investigating the disappearance of Ms Spence, said he phoned the London bank after seeing emails.
Det Con Brown said Ms Spence sent an email to the bank on April 11, 2011 claiming she had inherited bearer shares and received a reply the next day.
The trial before judge Lord Pentland continues.