Location of Orthocenter

Does the orthocenter always lie inside the triangle?

The orthocenter is not always inside the triangle. It depends on the type of triangle.

If the triangle is an acute-angled triangle, the orthocenter will always be inside the triangle (as shown in Fig. (a)).
If the triangle is an obtuse-angled triangle, the orthocenter lies outside the triangle (as shown in Fig. (b)).
If the triangle is a right-angled triangle, the orthocenter lies on the vertex of the right angle (as shown in Fig. (c)).