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Lavender can take up to 2 months to germinate. While you are waiting for it to germinate, I would keep the soil moist. While the plant likes dry soil, seeds need moisture to help germinate.

It may have gotten too much water and now has root rot. This article will help you diagnose that:
https://www.gardeningknowhow.com/plant-problems/disease/treating-root-rot-gardening-tips-for-housplants.htm

If that is not the issue, than it may be under watered. If it is in a container, it will need watering everyday outside when temps are over 30C.

Although rarely affected by pests, lavender is susceptible to small caterpillars and similar pests that feed on the leaves. Bacillus thuringiensis (Bt) is a naturally occurring soil bacteria that you spray on lavender and other plants. It is safe for the environment. It's available as a powder or liquid at garden stores everywhere.

This plant is a repellent to many harmful bugs. That is what makes it a good plant for the garden.

Yes you can transplant ,no it probably die .Ihave French lavender in the ground and in pots but i'm in so Tex. I found out I should have mixed in some crushed limestone with my mix. I'm not up on sweet lavender I have Grosso lavender .I would transplant but protect if were talking about the same type lavender.Go on line and find Annie lavender farms ,thats all they do . luck

This article should help: https://www.gardeningknowhow.com/edible/herbs/lavender/pruning-lavender.htm