The grain mill, downstream of the bridge and on the opposite bank, was still in use in 1917.
Taylor Hall was already a Hall by then. It is annotated as such on the 1917 Ordnance Survey map whereas it was shown as still being a woollen mill on the 1897 map.
Lint mills are a different matter altogether. There were several in the vicinity, mostly very small affairs. They didn't need much motive power as they just beat already soaked fibres for conversion from flax to linen yarn. That takes a lot less energy than turning great big grinding stones or racks and racks of spinning/weaving machines.
The Lennis Burn, as it is actually called locally, is misnamed on the OS maps as "Lin Mill Burn". I'm pretty sure that the mislabelling came about from a surveyor asking a local what the name of 'that' was, pointing to the river. The local seems to have misunderstood what was being pointed at and replied "lint mill". The glottle stop of the local dialect renders the 't' sound of 'lint' silent, so the surveyor seems to have transcribed the given answer as being the name of the river rather than the nature of the building beside it.
Once those errors go into print on the map the wrongness gradually becomes right as some people start to use the wrong name instead of the correct name. An example of that can be seen in the name of the late Aileen Scott's house as shown in the picture on message #10 of this thread. The house has never been a mill, but it is located next to the inaccurately 'named' Lin Mill Burn and has taken its name from that. Thus a name has been erroneously transferred from a real mill to a non-mill house.