I had to look up “pochade box.” (I see it is a kind of artist’s box. Funny that I did not know what that was since I originally went to college, back in 1969, to study art! Oh well.) Deep lids are not a problem. One standard way to make a box is to make a closed box and then to separate the top from the bottom by sawing through the box. You can make your lid as deep or shallow as you wish. No problem. If your box is dovetailed, you might plan ahead where you want to cut and make the pins or tails a tad wider at the point. This is done in the keepsake box mentioned by Mercified. It is also done by Paul in his toolchest videos. He cuts the top from the bottom in video 12. It sounds a bit mysterious until you see it done. There a probably a lot of short videos on youtube where people do it, almost always using a table saw — Paul, of course, does it by hand. But you can get the basic idea in just a few moments right here. https://www.youtube.com/watch?v=HEnaEw-rz8c.