Lettuce is easy. As long as it has nitrogen, it will be happy. General Hydroponics and Fox Farm are I think the two widest-used brands. You can also look at seed companies and greenhouse supply catalogs. Many of them sell bags of nutes in powdered form meant for greenhouse growers, although sometimes the quantities are large. Even something as simple as Miracle Grow will work. I have grown nice lettuce using just MG.

Please don't use Miracle Grow. the source of nitrogen in MG is Urea. Urea needs to be broken down by bacteria in the soil into nitrate that the plant can use. if you use MG in a hydroponics system you plants will be starved for nitrogen. hydroponics nutrients contain water soluble nitrates that your plants can use.

you can use any hydroponics nutrient for your plants. you're just growing lettuce so you don't have to worry about flowering or fruiting, so any nutrient with nitrogen will work, as long as it is hydroponic nutrient.

Since you are a
beginner, I would suggest going along the lines of a premade three part nutrient
solution, much like @cole_robbie is suggesting. I personally prefer General
Hydroponics because they come with easy to understand instructions on the back.

I would whole heartedly
agree with @kleeem on staying away from MiracleGro, not only for the reasons he
stated but because it can get very complicated trying to mix your own nutrients
since a solution like MiracleGro assumes soil will be providing some of the
nutrients.

Lettice is really easy
to grow so you should be fine. The three part nutrient will also allow you to
experiment with other plants as well, as you go with ease. They do make single
nutrients, but those can be tricky if you are switching between plants at a
later time. Might be fine and simple for now if you want to go with it.

Make sure that you get
a grow schedule from whomever you get your nutrients from or you could be fighting
uphill battles.

Also, I am sure you are
aware of this but watch the temp of your resivor. If it gets to hot or cold it
will inhibit that ability of the plant to uptake nutrients. I have seen some
people bury the bottom of their resivour and others just paint it white.