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Sounds as if it could use a good pruning. These articles should help: https://www.gardeningknowhow.com/edible/herbs/lavender/lavender-in-the-garden-information-and-growing-lavender-tips.htm, https://www.gardeningknowhow.com/edible/herbs/lavender/pruning-lavender.htm

You can split the plant in spring just as new growth appears. This article should help with pruning the plant: https://www.gardeningknowhow.com/edible/herbs/lavender/pruning-lavender.htm

It probably wouldn't hurt to cut it back and look for green within the stems, which should also be flexible. This article will help: https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm

Legginess in plants is often due to a lack of sufficient light, which indoors may not be enough. Generally, as long as the threat of frost has passed in your area and the ground has warmed enough for working, planting lavender outdoors this spring would be fine. These articles should help with growing and caring for your lavender: https://www.gardeningknowhow.com/edible/herbs/lavender/lavender-in-the-garden-information-and-growing-lavender-tips.htm, https://www.gardeningknowhow.com/edible/herbs/lavender/pruning-lavender.htm

Lavender is generally not pruned until it's well established in its second year or later. In addition, it is normally pruned in the spring rather than fall. Here is an article that you may find helpful: https://www.gardeningknowhow.com/edible/herbs/lavender/pruning-lavender.htm