The picture you've chosen of a water tunnel test at Onera nicely shows how the vortices generated at the leading edge of the delta wing wash over its upper surface and coalesce to form two big vortices, one on each side of the wing. Those vortices help the airflow in remaining attached to the wing so that lift can be generated till very high AoA, as it can be seen for example in the following plot taken from this NASA report:
The 62° delta wing tested at subsonic speeds generates lift till some 30° while a "standard" rectangular or swept wing would stall at maybe half of that angle.
is it possible that wingtip vortex can also produce vortex lift?
The same vortex phenomenon happens also on a "standard" wing but! their coalescence takes place well behind the trailing edge, where the wing is already finished and the effect of generating lift till very high AoA has therefore no time (or space) to develop.
Anyway this is not the only important characteristic of those vortices: in general, when a vortex rolls up along a direction parallel with the chord, it generates also a force aligned with it i.e. drag by definition. This drag is termed induced drag. The vortices seen on the delta wing make no exception: if on one hand they help the airflow in remaining attached, on the other hand they increase drag as well and quite a lot.
So it becomes now quite interesting to compare the polar of that delta wing with the polar of a standard swept wing (the plot for the latter is taken from this second NASA report):
Let's compare for example the points at $C_l=0.8$. For the delta wing it corresponds to a $C_d$ of 0.2 while for the swept wing it corresponds to a $C_d$ of some 0.07: that means that at the same lift coefficient a delta wing generates some three times more drag then a swept wing! That's why the Concorde had to takeoff with the afterburners on and that's
why try so hard eliminating it.