Hello & welcome.
Lavender is a Mediterranean plant
& so likes it Sunny--Hot & Dry.
to that end, water the plant
when the soil is almost dried out.
You can try to clip off the dead pieces.
It likes rich, well drained soil, and likes to be placed in a sunny location. To keep the roots out of standing water you could place pebbles in the drip tray and place the pot on top of the pebbles. This will help keep the roots out of any leftover water.
I hope this helps.