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How to list the first x files in each directory

# MWE

With the following tree:
```txt
l1
└── l2
    ├── d0
    │   ├── f0
    │   ├── f1
    │   ├── f2
    │   ├── f3
    │   ├── f4
    │   └── f5
    ├── d1
    │   ├── f0
    │   ├── f1
    │   ├── f2
    │   ├── f3
    │   ├── f4
    │   └── f5
    ├── d2
    │   ├── f0
    │   ├── f1
    │   ├── f2
    │   ├── f3
    │   ├── f4
    │   └── f5
    ├── d3
    │   ├── f0
    │   ├── f1
    │   ├── f2
    │   ├── f3
    │   ├── f4
    │   └── f5
    ├── d4
    │   ├── f0
    │   ├── f1
    │   ├── f2
    │   ├── f3
    │   ├── f4
    │   └── f5
    └── d5
        ├── f0
        ├── f1
        ├── f2
        ├── f3
        ├── f4
        └── f5

8 directories, 36 files
```

created by this script:
```bash
#!/bin/bash

path=l1/l2

mkdir -p $path

for dir in {0..5}; do
    mkdir $path/d$dir

    for file in {0..5}; do
        touch $path/d$dir/f$file
    done
done
```

# Problem 

How do I list the first three files of each directory?

First three being the first three alphabetically sorted.

# Tried

I can get each file via:
```bash
find l1 -mindepth 3 -maxdepth 3 -type f
```

but I can't find a way in the manual to specify the match depth.

The output from find is also unsorted, and so, the first three would not
be the first three alphabetically.


# Notes

My goal is to make a trimmed copy of a large dataset for preliminary,
quick testing as I develop my code. Performing this trim within the code
unneccesarily complicates the test code and will be a wasted effort as
it will be removed for the real deal. Without it in place, I am able to
test what will be the final product. 

The real target using the real dataset may be sub directories and not
files. In other words, "give me the the first 3 directories in level 2".