"The lion is sitting on its tail."
Translation:Lejonet sitter på sin svans.
Yes, if it isn't sin/sitt. For instance it must be Jag ger lejonet dess mat 'I give the lion its food', because I am the subject, not the lion.
For pets and similar animals, we often use gendered pronouns instead. We're more likely to use gendered pronouns for animals we feel closer to. So if you happen to know this specific lion a little better, you could use hans or hennes instead too.
But i wouldn't say "hon har ont i siått huvud" but "hon har ont i huvudet". Usually in swedish for body parts (and cell phones) it's "the leg" or "the head" and it's just understood that the part belongs to the subject of the sentence. So why does that not hold here?