Lettuce needs hardly any water when young and then lots once they take off, then only a little again when maturing heads so the plants don’t rot.
I’d try starting some single plants in cell flats and transplant when roots start to crawl out the bottom, the wet/dry cycle seems to be very good for young seedlings.
One other thing that can cause bitterness and stunted growth is N or K deficiency. I grow lettuce all summer here, the plants don’t get as big but as long as they are watered daily during the heat the quality is still good.
Pro-tip: lettuce is bitter because of the sap, harvest early in the morning before it rises, if still too bitter then store in the fridge for a day or 2 and the bitter compounds will be metabolized.