I bought two $20 lavalier smartphone mics to use in video interview.

I found the audio can clip if the speaking volume gets unusally loud, no matter what the gain setting in the recording app is set to. I suspect the preamp in the phone causes the clipping before it reaches the stage that controls gain. Could someone confirm this?

Using the same lavalier mic and a zoom recorder, I was able to record loud speaking voice with no clipping.

But since I have several old smart phones, and these lavalier mic only cost $20, it would be nice if I could make this combination work. Has anyone solved this problem?

It is unlikely that anybody can offer any practical response without knowing what you are talking about.
What microphones?
What phone?
What app?

I bought two $20 lavalier smartphone mics to use in video interview.

I found the audio can clip if the speaking volume gets unusally loud, no matter what the gain setting in the recording app is set to. I suspect the preamp in the phone causes the clipping before it reaches the stage that controls gain. Could someone confirm this?

Using the same lavalier mic and a zoom recorder, I was able to record loud speaking voice with no clipping.

But since I have several old smart phones, and these lavalier mic only cost $20, it would be nice if I could make this combination work. Has anyone solved this problem?
I think you answered your own question. Phones don't have anything approaching a professional pre-amp.
Probably moving the lav lower down would be the cheapest solution. If you're trying to interview guest at a wedding reception and they're shouting over the crowd noise, then you need to use something better like the Zoom H1.

Curtis Judd had a good video on the subject. He recommends the Rode SmartLav+ for $80

Another important point is what connector type the lav mics have. Most smartphones need a mic connection with a 4-pole mini connector, while audio recorders use a 3-pole mini connector.

If your lav's only have a 3-pole connector, you could try a 3-pole to 4-pole adapter when using with the smartphone and see if that helps the situation.

I give up using retired smart phones for audio recording. It was a neat idea but doesn't pan out.

The lavalier mic I bought is similar to rode smartlav+ in function and also has TRRS 3.5mm plug. I just bought a $25 adapter called rode vxlr+ that allows the mic, which needs plug-in power, to be used with phantom powered XLR input. Now I can use this mic with tascam recorder.

At first I resisted the idea of buying an adapter that cost more than the mic, but in the end it is the best quickest solution I could think of.

If you're making a living from this or plan to do so you'll quickly discover the amount of money you save trying to cut corners, is usually proportional to the pain and extra time you will have to deal with down the road.

You don't need to buy the best of everything but there is threshold you need to break to get into professional equipment. Spend on a decent wireless kit or get a good digital recorder and then you can concentrate on working, making money and building your business.

If you're making a living from this or plan to do so you'll quickly discover the amount of money you save trying to cut corners, is usually proportional to the pain and extra time you will have to deal with down the road.

You don't need to buy the best of everything but there is threshold you need to break to get into professional equipment. Spend on a decent wireless kit or get a good digital recorder and then you can concentrate on working, making money and building your business.

This.

Audio is half the final product! So it shouldn't be unreasonable to spend just as much on your audio gear as your camera gear.