diff --git a/spacy/tests/conftest.py b/spacy/tests/conftest.py
index 0fc74243d..3a5c8e451 100644
--- a/spacy/tests/conftest.py
+++ b/spacy/tests/conftest.py
@@ -337,17 +337,17 @@ def ru_tokenizer():
     return get_lang_class("ru")().tokenizer
 
 
-@pytest.fixture
+@pytest.fixture(scope="session")
 def ru_lemmatizer():
     pytest.importorskip("pymorphy3")
     return get_lang_class("ru")().add_pipe("lemmatizer")
 
 
-@pytest.fixture
+@pytest.fixture(scope="session")
 def ru_lookup_lemmatizer():
-    pytest.importorskip("pymorphy2")
+    pytest.importorskip("pymorphy3")
     return get_lang_class("ru")().add_pipe(
-        "lemmatizer", config={"mode": "pymorphy2_lookup"}
+        "lemmatizer", config={"mode": "pymorphy3_lookup"}
     )
 
 
@@ -423,19 +423,19 @@ def uk_tokenizer():
     return get_lang_class("uk")().tokenizer
 
 
-@pytest.fixture
+@pytest.fixture(scope="session")
 def uk_lemmatizer():
     pytest.importorskip("pymorphy3")
     pytest.importorskip("pymorphy3_dicts_uk")
     return get_lang_class("uk")().add_pipe("lemmatizer")
 
 
-@pytest.fixture
+@pytest.fixture(scope="session")
 def uk_lookup_lemmatizer():
-    pytest.importorskip("pymorphy2")
-    pytest.importorskip("pymorphy2_dicts_uk")
+    pytest.importorskip("pymorphy3")
+    pytest.importorskip("pymorphy3_dicts_uk")
     return get_lang_class("uk")().add_pipe(
-        "lemmatizer", config={"mode": "pymorphy2_lookup"}
+        "lemmatizer", config={"mode": "pymorphy3_lookup"}
     )
 
 
diff --git a/spacy/tests/lang/ru/test_lemmatizer.py b/spacy/tests/lang/ru/test_lemmatizer.py
index e82fd4f8c..d28f98044 100644
--- a/spacy/tests/lang/ru/test_lemmatizer.py
+++ b/spacy/tests/lang/ru/test_lemmatizer.py
@@ -81,6 +81,7 @@ def test_ru_lemmatizer_punct(ru_lemmatizer):
 
 
 def test_ru_doc_lookup_lemmatization(ru_lookup_lemmatizer):
+    assert ru_lookup_lemmatizer.mode == "pymorphy3_lookup"
     words = ["мама", "мыла", "раму"]
     pos = ["NOUN", "VERB", "NOUN"]
     morphs = [
@@ -92,3 +93,17 @@ def test_ru_doc_lookup_lemmatization(ru_lookup_lemmatizer):
     doc = ru_lookup_lemmatizer(doc)
     lemmas = [token.lemma_ for token in doc]
     assert lemmas == ["мама", "мыла", "раму"]
+
+
+@pytest.mark.parametrize(
+    "word,lemma",
+    (
+        ("бременем", "бремя"),
+        ("будешь", "быть"),
+        ("какая-то", "какой-то"),
+    ),
+)
+def test_ruk_lookup_lemmatizer(ru_lookup_lemmatizer, word, lemma):
+    assert ru_lookup_lemmatizer.mode == "pymorphy3_lookup"
+    doc = Doc(ru_lookup_lemmatizer.vocab, words=[word])
+    assert ru_lookup_lemmatizer(doc)[0].lemma_ == lemma
diff --git a/spacy/tests/lang/uk/test_lemmatizer.py b/spacy/tests/lang/uk/test_lemmatizer.py
index 788744aa1..616c36f48 100644
--- a/spacy/tests/lang/uk/test_lemmatizer.py
+++ b/spacy/tests/lang/uk/test_lemmatizer.py
@@ -8,12 +8,22 @@ pytestmark = pytest.mark.filterwarnings("ignore::DeprecationWarning")
 def test_uk_lemmatizer(uk_lemmatizer):
     """Check that the default uk lemmatizer runs."""
     doc = Doc(uk_lemmatizer.vocab, words=["a", "b", "c"])
+    assert uk_lemmatizer.mode == "pymorphy3"
     uk_lemmatizer(doc)
     assert [token.lemma for token in doc]
 
 
-def test_uk_lookup_lemmatizer(uk_lookup_lemmatizer):
-    """Check that the lookup uk lemmatizer runs."""
-    doc = Doc(uk_lookup_lemmatizer.vocab, words=["a", "b", "c"])
-    uk_lookup_lemmatizer(doc)
-    assert [token.lemma for token in doc]
+@pytest.mark.parametrize(
+    "word,lemma",
+    (
+        ("якийсь", "якийсь"),
+        pytest.param("зеленої", "зелений", marks=pytest.mark.xfail()),
+        ("розповідають", "розповідати"),
+        ("розповіси", "розповісти"),
+        pytest.param("телятові", "теля", marks=pytest.mark.xfail()),
+    ),
+)
+def test_uk_lookup_lemmatizer(uk_lookup_lemmatizer, word, lemma):
+    assert uk_lookup_lemmatizer.mode == "pymorphy3_lookup"
+    doc = Doc(uk_lookup_lemmatizer.vocab, words=[word])
+    assert uk_lookup_lemmatizer(doc)[0].lemma_ == lemma
diff --git a/spacy/tests/pipeline/test_pymorphy_lemmatizer.py b/spacy/tests/pipeline/test_pymorphy_lemmatizer.py
deleted file mode 100644
index a1a5f03f2..000000000
--- a/spacy/tests/pipeline/test_pymorphy_lemmatizer.py
+++ /dev/null
@@ -1,35 +0,0 @@
-import pytest
-import pickle
-from spacy import util, registry
-from spacy.lang.uk import Ukrainian
-from spacy.lang.ru import Russian
-from spacy.lookups import Lookups
-
-from ..util import make_tempdir
-
-
-def test_lookup_lemmatizer_uk():
-    nlp = Ukrainian()
-    lemmatizer = nlp.add_pipe("lemmatizer", config={"mode": "pymorphy2_lookup"})
-    assert isinstance(lemmatizer.lookups, Lookups)
-    assert not lemmatizer.lookups.tables
-    assert lemmatizer.mode == "pymorphy2_lookup"
-    nlp.initialize()
-    assert nlp("якась")[0].lemma_ == "якийсь"
-    assert nlp("якийсь")[0].lemma_ == "якийсь"
-    assert nlp("зеленої")[0].lemma_ == 'зелений'
-    assert nlp("розповідають")[0].lemma_ == 'розповідати'
-    assert nlp("розповіси")[0].lemma_ == 'розповісти'
-    # assert nlp("телятові")[0].lemma_ == 'теля' # pymorph2 fails
-
-def test_lookup_lemmatizer_ru():
-    nlp = Russian()
-    lemmatizer = nlp.add_pipe("lemmatizer", config={"mode": "pymorphy2_lookup"})
-    assert isinstance(lemmatizer.lookups, Lookups)
-    assert not lemmatizer.lookups.tables
-    assert lemmatizer.mode == "pymorphy2_lookup"
-    nlp.initialize()
-    assert nlp("бременем")[0].lemma_ == 'бремя'
-    assert nlp("будешь")[0].lemma_ == "быть"
-    # assert nlp("какая-то")[0].lemma_ == "какой-то" # fails due to faulty word splitting
-    assert nlp("зелёной")[0].lemma_ == 'зелёный'