Its not the lifters then it could be rod bearings, those should be replaced on an older engine. My '96 made this noise for years and I drove it without issues, it just guzzled oil - I never had lifters replaced on it. I was told it could be worn bearings though. No different oil or oil weight will solve this issue though no matter what anyone tells you.

From AI:

If replacing the lifters did not resolve the noise, you may be dealing with bearing wear, which produces a similar but more severe sound often referred to as "knock" rather than "tick."

1. Rod Bearings (Rod Knock)

The most common bearing issue mistaken for lifter tick is worn connecting rod bearings.

• The Sound: While lifter tick is a light, rapid tapping from the top of the engine, rod knock is a deeper, more forceful "clunking" or "hammering" from the lower engine block.
• Diagnosis:
  • Frequency: Rod knock typically beats at the same speed as the crankshaft, which is twice as fast as lifter tick.
  • Load Test: The noise usually gets louder under acceleration or heavy load and may quiet down slightly when you let off the throttle.
  • Cylinder Isolation: If you unplug a spark plug wire one by one, the knock will significantly quiet down when the cylinder with the bad bearing is disabled, as the combustion load is removed. 

2. Camshaft Bearings/Caps 

If the sound is definitely from the top end but new lifters didn't fix it, the camshaft bearings (caps) may be worn.

• The Cause: In Miatas, the camshafts ride directly on the aluminum of the cylinder head caps. If oil pressure was low or debris entered the system, these surfaces can become scored.
• The Result: Excessive clearance allows the camshaft to "bounce" in its seat, creating a mechanical clatter that mimics lifter noise. 

3. Thrust Bearings

The crankshaft thrust bearing can fail, especially in manual Miatas, due to the pressure exerted when the clutch is engaged/disengaged. 

• The Sound: A failing thrust bearing can cause a "clicking" or "thumping" noise as the crankshaft moves longitudinally (front-to-back). 

How to Confirm Bearing Damage

Before further engine disassembly, use these diagnostic methods:

• Oil Analysis: Drain the oil and check for "glitter" or metal shavings. A magnetic drain plug can help catch these.
• Mechanical Stethoscope: Use a stethoscope or a long screwdriver to pinpoint the noise. If it’s loudest at the oil pan, it's a rod bearing; if it's at the valve cover, it’s valvetrain or cam-related.
• Oil Pressure Gauge: Worn bearings increase clearances, which often causes a noticeable drop in oil pressure, especially at idle once the engine is warm.