Lavender: There are quite a few varieties promoted in your area and they are very similar. So we're sorry to say but we can't give you a positive ID from a photo. Your best bet is to take it to your local garden center for an 'in-hand' assessment.
Overwatering: The knats are caused by too much moisture in the soil, or poor drainage in the pot. Put outside for a day or two in partial sun and allow the soil to dry out a bit. The knats will usually work their way out The brown edges are a sign of age and should be removed so that the new growth a the base can come out fresh. Those plants in the mint family need to be cut back regularly to keep promoting new growth. They are what would call a cut-and -come herb.
Lavender (lavandula spp): Your plant belongs to the Lavendula genus, known for their fragrant flowers, finely divided aromatic foliage, and ideal for warm, dry climates. The are many species and varieties and some varieties are used to make perfume or potpourri. Others are used for herbs if raised organically. Needs full sun and although it is drought tolerant once established, will flower better if watered regularly. Does not do well with chemical fertilizers.
Lavender Problem: Lavenders need perfect drainage and succumb quickly if soils are overly wet. Let it go partially dry between waterings or cut it back and move it into a pot if your soil does not drain well. Consider a fungicide drench of the soil, too.
Lavender (lavandula sp): Your plant appears to belong to the Lavendula genus, known for their fragrant flowers, finely divided aromatic foliage, and ideal for warm, dry climates. The are many species and varieties and some varieties are used to make perfume or potpourri. Others are used for herbs if raised organically. Needs full sun and although it is drought tolerant once established, will flower better if watered regularly but allow the soil to dry out between waterings. Does not do well…
Spiderwort (tradescantia): Tradescantia is a popular garden plant, loved for its grassy foliage, blue, purple, or pink flowers, and easy care. It can spread over time, and prefers full sun and regular water. There are many native varieties available
Milk Thistle (silybum marianum): A nasty weed that will spread widely if allowed to go to seed. Can be hoed but might come back. This plant is on the invasive list and should be carefully removed and destroyed. The spines are very dangerous also. In a wild space it is quite beautiful and beneficial to bees and butterflies.
Geranium Cultivar (pelargonium): Your geranium is a sun-loving annual where winters are cold, but a perennial in mild winter regions. It is relatively drought tolerant. Water when the top inch of the soil feels dry to the touch and give it a full sun location. Comes in a variety of colors and is a very popular annual/perennial. Regular removal of spent flowers will encourage it to keep blooming.
Oxalis (oxalis vulcanicola): This appears to be an oxalis; it can be grown as a garden annual (in full or partial sun) or as a houseplant in a sunny window. Needs regular water. It is a much better behaved Oxalis than other varieties. Do not allow plant to sit in water as this may lead to root rot. Feed with a slow-release fertilizer formulated for container plants.