It depends on the theoretical question under investigation. Of course, the general idea regarding integration is that one method can provide information that the other can't, and so together we can get a better picture of a given function. Based on my experience with grant proposal submissions combining lesion and fMRI methods, some folks seem to believe that the best approach is to use the same task in the context of both methods. This seems quite reasonable. Healthy subjects may activate, say, the posterior temporal lobe and inferior frontal cortex while listening to words, and we may wonder what role these regions might be playing the task. We could then examine lesion data, where we might find that lesions to the posterior temporal lobe better predict auditory comprehension deficits than frontal lesions.
But this complete parallelism approach doesn't always work because a given task doesn't always translate well across methods. Consider a simple word-to-picture matching task which is commonly used in lesion studies. Patients listen to a word and then point to the matching picture in an array containing phonemic and semantic foils. Aphasic patients with unilateral lesions and auditory comprehension deficits, tend to make semantic errors on such tasks indicating a breakdown at some post phonemic processing level. Lesion data broadly implicate posterior temporal areas. It would be nice to use fMRI to provide further spatial resolution regarding the localization of the disrupted function. But if we simply import the picture-matching task into the magnet, we would see activations associated with all stages of the comprehension process, not just the level that is primarily disrupted in the lesion cases. So to provide the "converging" fMRI evidence that we are after, we would have to change the paradigm. For example, we might use semantic priming, or some other post-phonemic task in fMRI to try to selectively highlight relevant regions. If we found posterior temporal activations, this would be decent converging evidence.
In the grant proposals I have submitted, we used not only parallel-task integration approaches, (when possible), but also this other form of integration where the task necessarily has to change to answer the same kind of question. It was the later case that seemed to raise concerns among some reviewers. We were able to successfully argue our case in subsequent revisions with one proposal, but had less success with similar arguments with a different proposal and different set of reviewers.
I guess the upshot is (i) there's more than one way to integrate data from multiple methods, where the approach you use depends a lot on the specific questions you're asking, and (ii) if you are writing a grant that proposes cross-method integration AND you are NOT using a parallel-task approach, be sure to be very clear about the logic behind your approach because there does seem to be a parallel task bias among some reviewers.