When arising in the morning we are told in Halacha that we should rise up like a lion. My question is why like a lion? Why not rise like a bull or a horse? What is unique to a lion that we are supposed to emulate upon arising in the morning?
Lion is usually used as the animal that represents strength (see Pirkei Avot 5:20 יְהוּדָה בֶן תֵּימָא אוֹמֵר, הֱוֵי עַז כַּנָּמֵר, וְקַל כַּנֶּשֶׁר, וְרָץ כַּצְּבִי, וְגִבּוֹר כָּאֲרִי, לַעֲשׂוֹת רְצוֹן אָבִיךָ שֶׁבַּשָּׁמָיִם). Also note that strength in Chazal is not necessarily physical strength, but often an inner strength and the ability to overcome one's natural impulse. To overcome the trait of laziness and the temptation to stay in bed, it makes sense that one needs this characteristic of (inner) strength.
In addition to what has already been answered above.
The שערי תשובה on the opening סימן in שלחן ערוך that you brought in the question adds:
כארי. עיין באר היטב ועיין ט"ז שכתב שעיקר הגבורה הוא נגד היצר הרע ואמר כארי כו'. ויראה שהוא ע"ד שאמרו ביומא דף ס"ט נפק אתא כגוריא דנורא מבית קה"ק ולזה אמר שיתגבר כארי נגדו:
Like a lion. Over in the Be'er Heitev and the Taz it writes that the main strength that one needs against the Yetzer Hora is like lion. Like it says in Yuma 69 - 'A fire-like lion ascended from the Holy of Holies' and that's why it says that one should arise like a lion against him (the Yetzer Hora)
The implication is that in the same way the Yetzer Hora presents itself as a lion - we are charged to symbolically fight 'fire with fire' i.e. we too need to act like lions to overcome the Yetzer Hora.