you are right
obok + genitive
przy + locative
blisko is not as close as obok/przy. I think near, close to= blisko and next to/by /at = obok, przy
Obok and przy are sometimes treated as interchangeable.
obok us more side by side, while "przy" is more face to face.
For example the cupboard is "przy" the wall, but "obok" wardrobe.
the building is "przy" street, but "obok" the school.
when you eat you seat "przy" the table
As far as I know, English rather doesn't use "to stand" or "to lie" to talk about objects, so the most natural translation of the lamp sentence is simple "is". However, it's perfectly natural to say that someone is standing somewhere, so in such a sentence we'd prefer to keep to it.