Southern Ag Atrazine Weed Killer for St. Augustine Grass would be a good option as it is labeled to control dichondra and it can safely be applied to St. Augustine turf.
Lontrel Turf and Ornamental Herbicide is not labeled to kill ivy or vines. You may want to try spot treating the vines with Hi-Yield 2,4-D Selective Weed Killer. It is labeled to kill ground ivy and similar plants, although it does not list monkeygrass or liriope specifically as a tolerant species, so you should still be careful when applying it.
Lontrel Turf and Ornamental is labeled to control clover in ornamental plantings. Mazus is not listed on the label as tolerable but you can test in a small area to be sure it will not also harm it.
Lontrel Turf and Ornamental Herbicide is not labeled to be used on residential lawns. Most of the herbicides will only suppress the torpedograss for a short time. It is recommended to spot treat the torpedo grass with a non-selective herbicide such as Round Up Quick Pro and then reseed or sod in the treated areas. Solitare is one such herbicide labeled to suppress it and is safe for Centipede grass.
Lontrel Turf and Ornamental Herbicide is not labelled to be used on sumac and could injure it.
When using Lontrel Turf and Ornamental Herbicide for Dollarweed, the product label calls for ½ fl oz (15 mL) per 1,000 sq ft. The first thing you need to know when using an herbicide such as Lontrel Herbicide is that the exact amount of water you dilute it with is not important. It is only important to make sure you are using the correct amount of product per 1,000 sq ft of lawn. Use too much and you risk damaging your lawn, use too little and you will not get adequate results. To decide how much water you want to use, you should mark a 1,000 sq ft area, fill your sprayer with water ONLY, and start walking and spraying just as if you were doing the actual application of herbicide. When you are done walking and spraying the 1,000 sq ft area note how much water it took you to spray that area. That is the amount you will want to mix the specified amount of product with for each 1,000 sq ft area that needs to be treated.
Lontrel Turf and Ornamental Herbicide is not labeled for garlic mustard weed control.