I'm not aware of there ever being a cabin at Lavistown, I think it was always only two single lines running in from Carlow and Waterford to Kilkenny, together.
Navan Junction to Kingscourt Junction was, for a short time, a proper double-track line, with a cabin at Kingscourt Junction. Like a lot of cabins probably over-provided during the installation of block working and interlocking, (post-Regulation of Railways Act 1889), Kingscourt Junction had a short life.
Harpers block was installed Newry King Street to Bridge Street c1907, so the double-track was from Newry North to Bridge Street.
The Belfast Central was double from Central cabin to East Bridge too.