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# Python 3, 50 bytes

We can simply omit the lambda name since we don't refer to it anywhere in the lambda definition.

```python
lambda l:[l[:i+1].count(j)for i,j in enumerate(l)]
```
Example usage in the terminal:

```python
>>>(lambda l:[l[:i+1].count(j)for i,j in enumerate(l)])([1,1,2,2,2,1,1,1,3,3])
[1, 2, 1, 2, 3, 3, 4, 5, 1, 2]
>>>(lambda l:[l[:i+1].count(j)for i,j in enumerate(l)])([3,7,5,4,9,2,3,2,6,6])
[1, 1, 1, 1, 1, 1, 2, 2, 1, 2]
```
I tested this on version 3.8.5 but this should work on earlier as well as newer versions of Python 3.