Unfortunately, I've never done the daily tablespoon olive oil and fresh lemon juice flush, unless you count a homemade salad dressing with those ingredients. =)
However, I have come across numerous posts on various sites which refer to it as a more of a "tonic" or "tune up" that's helpful *in addition to* the more intense oil and citrus flush.
Considering the two basic ingredients are the same as for the more intense flushes, taken all at once in the morning (as suggested on the page) could induce a mini-flush action. Logically, taken in the smaller separate doses at meal times they might help with digestion. Since lemon juice is healthy and olive oil is healthy, taking fresh squeezed lemon juice and a tablespoon of olive oil daily shouldn't be a problem for most people (except those who have reactions to either or both.)
It may be a very good 'introduction flush' to find out how your body will respond to the olive oil and lemon juice.
Since I have NOT actually followed the routine, I can't say what actions it actually takes. However, I *suspect* that it may be better at toning the liver and gallbladder and removing chaff and sludge than it is for removing 'stones.' Getting that gunk out is just as important! The sludge and chaff interfere with the efficiency of the organs and may form into the 'stonelets' which in turn form into 'stones.'
For actually getting the nasty 'stones' out, especially if large 'stones' or a lot of compacted 'stones' are suspected, I personally prefer some method of both softening the 'stones' and dilating or relaxing the bile ducts followed by a large powerful 'push' at the end. From my understanding of how the components of a flush work, the more intense flush would be more likely to get the larger 'stones' out.
Hopefully, someone who's done the daily tune-up flush for a while will speak up with some real world experience. =)