Here is a reference describing how lentiviral shRNA has been used to stably transduce monocytic cells: Unwalla, H.J. et al. Negative feedback inhibition of HIV-1 by TAT-inducible expression of siRNA. Nat. Biotechnol. Dec, 2004 22(12), 1573-8. Epub 2004 Nov 28.1
We suggest optimizing your experimental conditions with the TurboGFP Control Virus (Product No. SHC003V). You can easily see the transduction efficiency obtained with different lentiviral MOIs in your cells.