Pass parameters to pytest.lazy_fixture

My current situation is the following: I have a class C to be tested. To do so, I have a class TestC that (besides the tests) has a fixture f that creates an instance of C. Now, I have one test that checks how Cs interact. I'd like to invoke the fixture f twice, at best with different parameters. I thought that I can do that with lazy_fixture, but I'm not sure if I can pass parameters that way. What I'd like to achieve is

import pytest
class Test_Test:
    @pytest.fixture(params=[0])
    def f(self, request):
        print(request.param)
        return request.param
    
    @pytest.mark.parametrize(
        ['arg1', 'arg2'], 
        [
            pytest.lazy_fixture('f', params=[1]),
            pytest.lazy_fixture('f', params=[2])
        ]
    )
    def test_1(arg1, arg2):
        assert arg1 == 1
        assert arg2 == 2

which of course does not work, but hopefully makes my intention clear.

Is something like this possible?