Hello atulbaliga,
Water culture systems are very good for starting seedlings, but there are a lot of variables. I have a feeling that you haven't seen roots coming out the bottom mostly because of the sponge cube. Some sponge materials can be hard for the roots to grow through, and just take longer to do so.
With that said I have some other concerns.
1. It's hard to tell in the pictures but at least one of those pictures looks like one of those sponge cubes is saturated with water. The sponge material should be damp but not soaked. Some sponge materials soak up moisture easy and others not at all. So the actual material you used for your sponge cubes could be a problem not only because it may be tough for the roots to get through, but also because it may be sucking up to much water.
2. Related to #1, your water level may be to high causing your cubes to become saturated. Again the type of sponge material is going to be a huge factor in how much water it sucks up.
3. Your
nutrient concentrations are to high for seedlings that small. For seedlings that small I wouldn't use anything more than 1/4 strength.
4. I agree your pH is slightly high, not too much, but I would try and get it down closer to 6.0
5. Your water temp is to high, especially for the lettuce that is a cool weather plant. You want to get your water temps closer to 70-75 F ( 21-24 C). High water temps cause heat stress for the plants, and is especially hard on delicate seedlings.
5. Your lighting may be adequate for now provided the
bulbs are close enough to the plants, but will need to upgraded once they get bigger than seedlings.
P.S.
Using foggers can be problematic and tend to have issues. First they have been known to increase the odds of fungus and fungal disease on the roots. Second while the fog can look thick, there is very little actual moisture in it. The fog is basically dry and can very easily deprive the roots/plants from getting moisture they need, especially the bigger the plants get. Third the pads can easily clog and need replacement very often. Make sure to get Teflon pads if you do because the Teflon pads don't clog as easily.