Can we lead SPVs outside of our fund if it doesn't fit our thesis?

It may be possible to lead SPVs outside of a fund manager's Fund - however it is generally not recommended. 

Fund managers owe fiduciary responsibility (and usually a stated time commitment) to the Fund and its limited partners - so any activities that might come into conflict with these obligations could potentially become a conflict of interest. 

Even if the SPV is outside of the Fund's thesis, best practice is to disclose any such intended investments up front to limited partners and to clear each such SPV by a limited partner advisory committee. Managing these may be time consuming and not worth the additional effort - limited partners may also believe there is a misalignment of interests.