Should it be “cheaper price” or “lower price”?

It’s almost the same, and both are used constantly today interchangeably to mean the same thing; but, there are subtle differences.

cheap   adj: at low price, worth more than cost.
adverb: at or for a low price

low   adj: from top to bottom, below average in amount, extent, or intensity; small:
adverb: in or in a low position or state

cheap and low are synonyms for each other and synonyms for inexpensive.

In both sentences, the root words low and cheap are being used as adjectives. The connotation one over the other is, getting something cheap, you to get at a low price, and the item itself was worth more than the cost.

Low price might make someone believe they are getting something cheaper. Stores often trick buyers by offering items at a ‘lower price’. This, to make the buyer think the seller is selling something cheap; but, saying you paid a ‘lower price’ for something doesn’t make the item itself worth more than the cost.

Again, they are synonyms of each other. Just remember the adjective definition difference that separates cheap from low.

source: word definition cheap, low (www.dict.com)