When I was asked for an example of lesser shirk in class #7, I gave the example of: taking an oath by other than Allaah, for someone who does not revere the one he has sworn by as much as he reveres Allaah.
In support of this understanding, below are the words of Shaykh Ibn 'Uthaymīn - may Allaah have Mercy on him - on the topic (in Arabic):
Chapter: taking oath on other religion than al-Islâm and the Nabî sallalahu alayhi wa salam said 'whoever takes an oath on al-Lat and al-'Uzâ, let him say, La Ilaha Ila Laah, and that he did not call him a kâfir.
It was narrated to us by Mu'allâ b. Asad from Wuhayb from Ayyûb from Abî Qillaba from b. Dahhâk who said that the messenger of Allâh sallalahu alayhi wa salam said:
"whoever takes an oath on other than the religion of al-Islâm he is as he has stated. And whoever kills himself with a thing he will be punished with it in fire of Jahanam. Cursing a Mu'min is similar to killing him, and whoever accuses a Mu'min of kufr it is as if he has killed him."