Can contacts correct strabismus or lazy eye the same way glasses do?

It depends. Contact lenses cannot be used for prism correction of strabismus. Glasses are the better choice for this. For lazy eye, in some cases contacts can work well to correct vision in the lazy eye. It depends on the cause of the lazy eye. See your local ophthalmologist for a thorough exam.
Yes. Contacts can provide the optical correction part of the treatment especially at distance but may need to supplemented with reading glasses. Patching or cycloplegia of the stronger eye may still be required for lazy eye stimulation.