Isolated flues improve the draw.

Do we need to insulate when we fit a chimney liner?

If the chimney is exposed (on an outside wall), or
the stack is particularly tall, or
the flue is of a large diameter

then the answer to the proposed question above is a definite YES! Insulated liners keep the flue gases warmer, increase the upward speed of those gases and help prevent condensation.

Otherwise it is not necessary. The air between the liner and the flue will insulate the liner.

However, it is not difficult to insulate a liner (just adds cost) so it is up to you. 

Fitting is straightforward. Instead of feeding it down the chimney you haul it up the chimney. The person at the top has to have a very secure platform (e.g. scaffolding). A cherry picker might work but add the liner and wrap weight to the maximum allowed by the cherry picker.