Is there a welldefined nonholomorphic indexraising operator $V_l$, taking index$m$ JacobiMaass forms to index$ml$ JacobiMaass forms (same weight), analogous to the holomorphic operator defined in EichlerZagier, p.41? I haven't found it in the literature yet.
It may well be that no explicit expressions have been written down for the corresponding operator for JacobiMaass forms, but the analogous operators surely exist and behave reasonably, for the following reason(s). The EichlerZagier operator (and MaassShimura operators, in other contexts) are incoordinates expressions for differential operators coming from the enveloping algebra of the Lie algebra, regardless of the weight/index and/or holomorphy/waveform features, which would refer to the (irreducible or not) representation in which we are "moving around". That is, the intrinsic prescription of the operators (as opposed to the formulaic/incoordinates description) does not depend on the holomorphyorwaveform feature, nor upon the index and/or weight. Yes, the expressions for the operators certainly depend, but this is in principle a secondary issue. Thus, one can be reassured that it is possible to obtain the desired operators, and be assured in advance that they have the expected/desired properties. 

