Can a lawsuit settlement be taxed?

Yes.  Settlements are taxed or not according to the type of income they represent.  For example, a settlement for unpaid wages is taxed like wages.   Settlements for physical injury are not taxed.  Settlements for emotional distress are not taxed if the emotional distress was related to a physical injury, but are taxed if the injury was purely emotional.  Punitive damages and interest are taxable.  A settlement for physical damages to property is taxable if it exceeds your original cost to purchase the property.  Other settlements will follow the same general principles. 

Lawsuit settlements may or may not be taxable.  Settlements may be taxable in part.  So much depends upon the nature of the injury and how the settlement was constructed.

You may or may not be provided with IRS forms to report taxable income.

This IRS FAQ provides a good overview of this issue.