I am a bass player for over 35 years. Also play guitar. I have worked on my own electrics, setting intonation, etc. I have an acoustic. When I tune it, the low E, fretted at the 2nd 3rd frets are sharp. I checked on a tuner. Do I need to lower the nut where the E passes. Thanks in advance.
Depends on several factors. If the action is high, pressing a string anywhere will sharpen its pitch due to it being stretched. It will show up more at the lower notes. That high action could be due to the nut being too high, or the neck relief being too great, or the bridge being too tall. Or all of these.
Old strings sometimes do strange things, so a change may be all it needs. Tuners sometimes need a second to settle, and often show sharp initially.
The intonation could be way out on only that low E string. Check it's good using 12th and 19th fret harmonics. Last ditch effort - it may be a duff guitar, so take it to a luthier for checking.