Remember that a piano is considered to be a stereo instrument, in that it has width, so an arpegio played from the lowest to the highest note produces a sound that moves in space. Pianos are also designed to produce sound that is properly balanced at a distance. The sound comes from the strings, the sound board area, and other places. When you mic internally, you need to balance all this to produce a realistic sound. Sticking a mic inside a lid on full or short stick produces something that can be amplified, for live or TV use, but it doesn't sound right. Pianos all sound quite different, and if the sound between two brands can be heard by ear, then miking them up badly can make them all sound quite similar. With mics made in batches, there are often differences in the frequency response between versions made at different times, and these can make quite audible differences as the pianist plays across the instrument's range. It isn't too obvious in mono, but in stereo there's an odd kind of image shift as the player goes in one direction through a frequency range.

Sound on Sound magazine has had several excellent articles on mic selection and recording techniques for piano and there article database is available online. Here's one good one on recording a concert grand ...

Piano Recording

and another on micing uprights ...

Recording Techniques For Upright Piano

I achieved outstanding results just recently recording a jazz quartet.

I simply poped the lid open, placed a stereo mic on a boom at about 18" above the
center of the harp and Bingo.

Sounds very good.

Used a Rode NT1 Stereo mic with the default mic pattern.

NT1 ????? That's not a stereo mic nor a variable pattern mic. What did you use?

I agree with the Paul J post.

I recorded a piano solo a few weeks ago. I was lucky to have been there during the practice to feel out the mic placement and set levels. Without being there for a practice, I don't see how you would set this up. Be careful to not set levels too high as there can be a large dynamic range.

The best sound in that case with that piano was about 2 feet away from the piano and 1 foot above the plane of the top of the piano, which was open. The mic was set to XY position. I think I would have had more depth if the mic was back another foot without sacrificing ambient. Live & learn.

I would not get extremely close as others suggested. If you have time to do a setup before the actual event, it's pretty easy to find the general best sounding spot with good headphones.