"least" vs. "lowest"

Solution 1:

low - lower - lowest

little - less/lesser - least

A price is a level of cost, and refers to value within a scale. It can be high or low, or any variant thereof, but not least. You wouldn't say "the least rung" to refer the bottom level of a ladder, you'd say "the lowest rung."

If, instead of "level of cost," you referred to the cost itself, you could say "least cost." Likewise, you could say the "least high rung" in the case of the ladder.

Solution 2:

Least is the superlative of little (Merriam-Webster, Wiktionary). Little — less/lesser/littler — least/littlest.

The superlative of low is lowest (Merriam-Webster, Wiktionary). Low — lower — lowest.

A price can be low or small, but it usually can't be little (that usage is metaphorical), as can be seen by consulting the British National Corpus and the Corpus of Contemporary American English:

                  BNC  COCA

little price       0     4
  (metaphorical)   1     2
small price       64   329
low price         80   355  

Solution 3:

The "least" possible price is zero.

Stores will not advertise the above. Instead, they will advertise the "lowest" possible price that they can accept (and hopefully make money, but they are "taking their chances.")