Need help with lettuce

Hi,
I am struggling to grow some lettuce.
I sow indoor some butterhead lettuce seed at the end of march and a second batch after two weeks, they both germinated within a week but then problems occur. The first batch of seedlings developed quickly becoming very tall and falling. I thought that was a light problem so I payed a lot more attention at the second batch, once they germinate i put them in the greenhouse to get as much light as possible, they produced lots of leaves but then they start to collapse. I thought was too hot inside so I took them out in sunny days but they are still floppy and no head is present.

What I am doing wrong?
Did I get the wrong lettuce for the period?
There is a lettuce that can grow in the summer?

Help

 

I tend to think you are expecting too much, just guessing.
Lettuce need full light and cool growing conditions.

The greenhouse should be fine, but perhaps too hot on sunny days by now.

Are you pricking them out singly?

 

Maybe you are right. But to me they look not healthy at all
The seeds were sowed in single cell 8 for batch.

 

But are you expecting a hearted lettuce grown from a cell?
How big is the cell?

A picture would be good.

 

They are the small cells for the seedling. I was planning to transplant them when big enough.
Is better if I plant them in big pots?

 

Well you need to grow them on for a couple of months before expecting them to heart up, and they will need a lot more root space in the meantime.
I'd grow singly if you want a hearted lettuce.

 

I transplant them in a raising bed outside the greenhouse which has been covered with a light fleece.