A few notes. Oil causes deterioration of the rubber hoses quickly, if you see them 'sweating', replace them all. Oil also probably speeded up failure of the water pump seal in ours.
There are other noises that can fool you by sounding like noisy lifters, such as a rattling belt idler damper shock. However, the lifters are hydraulic, so they can jam.
Buy a replacement belt idler tensioner unit and keep it handy, if you don't know it was already recently replaced. These work by applying a torsion to a rubber bushing, and WILL deteriorate and fail at an inconvenient moment - usually at the last step of some flawless engine repair project. That leaves the car undriveable until replaced.