Either one of those might be of benefit if your soil lacks an active Soil food Web. However, for either one to be of much use the soil your lawn is growing in needs to have an active Soil Food Web to convert those materials into something the plants growing in that soil can utilize, ie. nutrients.
Does your soil have an adequate level of organic matter?

"Does your soil have an adequate level of organic matter?"

Probably not. The house was built less than 2 years ago in a new subdivision. Since I've become more interested in my lawn, I've been paying attention to other lots as they have homes built on them. Basically after all the large trucks tear up the yard (cement trucks, brick layers, etc.) the contractor levels out the yard with a lot of sand.

Depending on where you dig in my yard, it's either mostly sand or a layer of clay then sand. I'm in the process of topdressing the lawn with compost, but I have only been able to do half of the back yard so far.

What I have seen happen, around here, with new developments is someone comes in and strips the "topsoil" to go to some other development and then after the houses are built they haul in more "topsoil" and spread a thin layer and either lay sod or seed that. Then people try to keep that lawn growing by pouring a lot of "fertilizer" on it which can make for a lush green, but sick lawn with numerous problems that then need pesticides to control.
Short of tilling in what yuu have and starting over spreading compost is a good idea, mulch mow the grass to recycle in place those grass clippings which will help add more organic matter to the soil. If you have deciduous trees those leaves that fall from them every year can be mulch mowed in to provide evenmore organic matter.
What organic matter will do in sandy soils is help keep moisture and nutrients in the root zone so the grass plants can be fed by the soil bacteia that digest that organic matter. In clay soils the OM seperates the soil particles so the plants roots can move about more freely and makes moisture and nutrients more readily available.
Compost tea can provide some bacteria, and nutrients, tht would then feed on the organic matter in the soil. However, soils lacking sufficient levels of OM won't have much of anything for those bacteria to feed on so spraying the compost tea would be, largely, a waste of time, energy, and maybe money. Molasses can provide a food source for soil bacteria, if they are present because of adequate levels of organic matter. Spraying molasses onto soils lacking sufficient amounts of organic matter will not do much except waste your time, energy, and money.

canselmi, I agree with you. Molasses is more effective and easier.

You might want to read the Organic Lawn Care FAQ at the Organic Gardening forum. Then come back with more questions.

I think you can buy compost tea - that would remove the time/effort element of that option.

Where in Texas are you? In the DFW Mid-Cities, I prefer to shop at Strong's Nursery on I35 in Carrollton or Marshall Grain on 121 in Grapevine. Both have knowledgeable employees and a decent selection of organic products.

I've bought Ladybug brand bagged products at both locations.

~ freshair

I'm just south of Houston.
I am having trouble finding a feedstore. There is a Tractor Supply Company out in Katy, which is the closest I've found so far.