In the later '60s at least it was 0030 from Lime St and called at Crewe, Stafford, Tamworth, Nuneaton, Rugby, Northampton and Bletchley. The last Liverpool Euston was 1830, although by catching the 2240ish local to Crewe and a wait there you could catch the Barrow sleeper.
Chasing steam both this and the Manchester were useful trains, and the slow journey time was not important as you were warm and comfortable.
They may have been useful to get to London comparatively early (the first Euston departure from Lime St was 0830) but equally so for a later evening departure. Oddly, the down services had only one call (Stafford on the Liverpool and Stoke on the Manchester)
There was a network of overnight long distance trains and they were certainly useful for spotters wanting to make the most of the day - return halves of day returns were valid on the next day's strains such as these, and sleep was usually possible. My own most adventurous use, making the most of a week's 'Freedom of Scotland' ticket, involved catching an up sleeper (day coaches!) from Glasgow or Perth each night then, after a short nap at Carlisle, returning on the first down one, to avoid the outlay on B&B. Sadly, on the occasion I caught a Carlisle-Edinburgh (Waverley Route) train I fell asleep at Kingmoor, was woken briefly by a jerky stop at Hawick, and the next thing I saw was Waverley. Still undecided whether it counted as route...