How does underexposure with correction in Lightroom comport with the admonition to expose to the right. They seem at odds.
They aren't.
Underexposure always reduces the analog signal signal-to noise ratio. Exposure only depends directly on shutter time and, or aperture. This means using practical shutter times and, or apertures often results in unavoidable sensor underexposure. There are two very different ways to compensate for sensor underexposure.
At the camera's native (base) ISO maximizing exposure (shutter time and aperture) maximizes the signal-to-noise ratio for the data. By coincidence maximizing exposure produces an expose-to-the-right histogram. Using a tripod with static subjects means the sensor exposure can be maximized. But subjects in motion require shorter shutter times. Then practicality demands sensor underexposure.
When practically requires underexposure, at the native ISO setting the rendered image will appear too dark. There are two ways to increase the final image's brightness. One is to increase the brightness digitally in post-production. The other is to increase the gain of the analog signals before they are digitized in-camera. This is accomplished by the setting the camera's ISO setting above the native value.
In the first case, the in-camera histogram will not be biased to the right due to sensor underexposure. In the second case the histogram may
appear to be biased to the right. But it is identical to the first histogram. Increasing ISO also changes the exposure index calibration which simply shifts the histogram scale.
In the first case the histogram is a guide to avoid exceeding photo-diode full-well capacity. But in the second case the histogram becomes a guide to avoid exceeding the analog-to-digital converter's maximum signal threshold (clipping). These are very different situations.
In low light underexposure is often unavoidable. For some camera designs, increasing analog signal gain after the shutter closes increases the read noise levels. Underexposing at a lower ISO and increasing the brightness in post-production will result in cleaner shadow regions. However, now the best possible post-production rendering requires using raw files. In-camera JPEGs lossy compression destroys some of information needed to properly brighten the image.
With ISO-invariant designs the read-noise is essentially constant with respect to ISO setting. Shadow region SNR is not affected by read noise as ISO increases. One can use base ISO, raw files and just set the shutter time and aperture as needed. The only concern is exceeding sensor full-well capacity in bright light. Otherwise the histogram and, or meter can be ignored. When underexposure becomes unavoidable it will be impossible to clip the ADC. Image brightness is optimized in post-production.
Underexposure always increases the relative photon noise level. Camera ISO settings (electronic gain) have no impact on photon noise levels. Since read noise is essentially constant, the noise levels for ISO-invariant cameras are dominated by changes in photon noise. Otherwise, both read noise and photon noise degrade IQ as underexposure increases and the ISO setting is increased to brighten the rendered image.