My shul has statues of lions holding a Luchot display on top of the Aron, davening towards the statues make me uncomfortable. Is this a halachic problem?
Your question shows quite bit of sensitivity, and there is discussion among the poskim if it is permitted to have the lions there. Indeed a number of poskim prohibit making such lions on the Aron Kodesh, and indeed in many shuls they don’t have such lions. There are however poskim that are lenient about this, especially if it is only a profile picture of the lion, since it isn’t a picture of a whole lion.
It is interesting to note that the discussion among the poskim is regarding the prohibition to make images of celestial beings, which would include the picture of a lion, as there is an image of a lion on the kisei hakavod. There is also mention of your issue that we are bowing to it. R’ Eliyashiv however said that although it is improper to put them there, it isn’t really considered bowing to it, because the two lions are facing each other holding a crown of the luchos, and not facing the people.
Chida- Birkei Yosef- 141, Shevet Halevi 4-95, Minchas Yitzchok (Likutei Teshuvos 69), Yechave Daas 3-62, R’ Eliyashiv quoted in Ashrei Hoish Y:D pg. 95. Also see Igros Moshe Y.D. 2:55, who is lenient about this. Also see Divrei Yatziv Y.D. 1:38, Machaneh Chaim Y.D. 2:29:page 95.