I have recently purchased this inside plant, and some of the lower leaves have started to brown. I have watered, fertilised, and repotted this plant with new topsoil to see if it may improve the health... Once the leaves have started to brown, should I cut off, or leave?
Leave them on, and water WAY less. This is the start of a fungal infection, which is usually caused by overwatering, or not allowing the plant to dry out between waterings.
Use a fungicide to help combat the issue. This article will help: https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm
When in stress, it is best not to fertilize plants. Especially if these have been freshly repotted into a potting mix. Most contain more than enough nutrients, and adding more will only add to the stress of the plant.
Now, let's get back to that soil- That is an Asplundia which is epiphytic. This means that they don't actually reside in soil, but a soilless mix of bark like an orchid would. They grow attached to trees, or at the bases of them in nature.
Here is an article that will help you to care for these: https://www.gardeningknowhow.com/ornamental/flowers/asplundia/asplundia-information.htm