The first and most obvious reason for lining is if your chimney leaks ie. You get smells in the bedrooms and/or loft space or if there are tar stains on internal plasterworks or external brickwork.
If required a CCTV survey and smoke test will determine the condition of your chimney, answering all kinds of questions and enable the most appropriate solution to be specified.
The second reason concerns the physics of burning wood in a stove. A chimney needs to be warm to allow the stove to draw properly and prevent the rising emissions from cooling and condensing, which over-time leads to the build-up of solidified tar deposits. The construction of a chimney is likely to be of stone, brickwork or lined with clay and of a wider diameter than is suitable for a stove; these chimneys do not warm sufficiently, cool the stove gases and therefore lead to formation of condensates and tarring.
The installation of a stainless steel flue liner helps to maintain flue gas temperature and most stove manufacturers require that the chimney has a suitable liner of the correct size and specification to ensure safe and efficient operation of the stove.