As recently as around 10/03, I recall seeing a mention in LaQuinta's newsletter that the MasterCard was still available. It was issued by Citicorp, but has never been mentioned on Citi's web site. Don't know why it is so low profile; perhaps it is issued by one specific department of Citi.
LaQuinta hotels have/had application forms. For now, I would just call Citi at (888) 253-1350 or LaQuinta themselves to verify that the card is still available.
My recollection of the card was that the earning ratio was rather poor. You had to spend something like $11,000 in order to earn a free night. For that kind of spend on the Starwood AMEX, for example, you could end up with a much nicer hotel.