Unfortunately I'm not much of a plant physiologist, but here's what I was able to dig up.

Lettuce seeds get activated for germination through light signals. Light is sensed through a receptor family called the phytochromes (similar to the chlorophylls).

Phytochrome can absorb light, which changes its structure. There are two forms of phytochrome - active (phytochrome that absorbs far red light = Pfr) and inactive (phytochrome that absorbs red light = Pr.)

In red light, phytochrome in the form of Pr (through absorbing red light) changes to Pfr. This is the active form which can translocate into the nucleus and actually cause transcription of genes, which eventually result in germination. Thus phytochrome acts both as a receptor that senses light and as a transcription factor.

It's important to remember that light has both red and far red light, thus will be playing with the ratios of Pfr and Pr.

In full light, there is more red than far red (thus causing a higher amount of the active form Pfr.) This is why seeds may need light to germinate. In the soil this ratio is reduced, but there is enough red light to convert enough inactive phytochrome to active phytochrome (depends on how deep the seed is planted; which is why it's important not to bury your lettuce seeds to deep.)

Apparently, depending on the seed lot, there will be some lettuce seeds in the bunch that will germinate in the dark, because they are not as sensitive to light (higher amounts of Pfr compared to Pr ... I'm not sure how this occurs.... genetics and a bunch of hand waving?) I'm also uncertain as to the effects of other hormones (i.e. giberrelin, ethylene...) on germination in lettuce.

Germination can occur in the dark with other species of plants. Typically these are the hard seed plants (have hard coat so aren't really light accessible until after seed germination.) These would also be the seeds that don't mind being buried deep in the soil. I guess the lettuce seed coat is thin; thus it can respond to light.

As far as water goes, it seems that water does play a role in the events downstream of the Pr => Pfr conversion. What exactly it does, I'm not sure anyone knows. Perhaps diluting out inhibitors of germination?

Water doesn't play exactly the same role as in barley activating giberrelin.

Here is a paper from Pubmed, how higher water content enables the response to red/far red-light, lower water content makes the seed insensitive to light ...
read here.

The seed does have appropriate stores to germinate (found in the endosperm). The amount it has stored away varies depending on the plant. Seeds that can be buried far under ground, would have more storage than seeds that need to be buried close to the surface. The farther they have to travel to reach light and be able to photosynthesize, the more food they need stored away.