Is my leaning twin-trunk tree still structurally sound?

If the angle of the lean of the tree appears to be changing, the tree could be in the process of failing structurally. This is not uncommon following root damage. Decay organisms can invade damaged roots that can structurally weaken the tree causing it to fall.

There are several methods to determine if the angle of lean is changing. You should contact a consulting arborist who is qualified to evaluate the tree and determine if removal is warranted or if other treatments could reduce the risk of failure to acceptable levels.