They got their "source" originally from a twitter feed, which then sourced a PBS transcript, which a brief mention of a 2008 article in the Journal of Risk and Uncertainty, which is misrepresented by the PBS commentator Jeffrey Brown.
The actual article is
Myopic Risk seeking: the impact of narrow decision bracketing on lottery play.
[link to sds.hss.cmu.edu
This study was not trying to find out what percent of the poor bought lottery tickets, and there is not any info about households less than 13,000 buying 9% of their income in tickets , but they do mention several papers on lottery statistics offhand, it's possible one of these papers has the statistic, not so far I've been unable to find it.
The closest is this line
"Approximately 50% of households with an income less than $25,000
play the lottery, and among the households that play, the annual per capital expenditure is upwards of $550 (Clotfelter et al. 1999)"
but it's not clear if the $550 is the average for all Household or, only those of 25,000 and lower. Still it's not 9%, especially if you remember that 50% of the poor do not play at all.
One paper on lottery statistics says that the annual amount spent on lottery tickets broken down by income brackets doesn't vary much, from $125-$145. Of course this means lower income brackets use a higher percentage of their income, but that's a given for anything the poor purchase.
I also found several blog posts pointing to the 2008 journal article in Risk and Uncertainty, saying it says the same thing that the PBS douchebag did when it in fact does not, so these "journalists" are not checking source, including the schmuck from PBS