In this report we show using numerical simulations that, with judicious choice of pump and fiber parameters that it is possible to achieve lasing at wavelengths longer than 4 µm from the 6H11/2 6H13/2 laser transition of Dy3+ using an indium fluoride (InF3) glass host. The key issue for this transition is the short lifetime of the upper laser level of 1.25 µs relative to the long lifetime of the lower laser level which is 640 µs. Whilst continuous wave (CW) cascade lasing at 4.4 µm and 3.3 µm could be achieved, the large pump power requirement at threshold of >30 W is impractical. Pulsed pumping combined with gain switching however offers a viable alternative. We calculate that 200 ns, 160 µJ pump pulses launched into InF3 fiber could deliver 15µ J output at 4.4 µm. Scaling of average output power is constrained by population buildup in the lower laser level. Boosting the output power by quenching this lower level lifetime using OH-1 or Tb3+ co-dopants are explored as ways overcome this limitation.