Yes you can do it but need to exercise some precaution: The LV winding that was intended by design to be the secondary winding, will serves as the primary & the value of the magnetizing inrush current actually will be greater than expected. When a transformer is reverse fed, the taps move to the output side and so their operation is reversed. Taps will control the output voltage so chances of over excitation will be there. This is not serious concern till the input voltage variation is within limit. OC voltage of the winding which is supposed to be the secondary will be higher than the nominal voltage. This is to allow for the drop in the winding so that the nominal voltage will be present when the transformer is loaded fully. The degree of change in the secondary voltage is expressed as the transformer's regulation; the lower the figure the better. Using the transformer in reverse you need to increase the applied voltage to the secondary which will act as primary when reverse fed.
First: You'll need to verify that the new input voltage is the same per coil winding as the original impressed across the coil to ensure the flux density in the core is per original spec and to ensure the insulation system still falls within design specs as far as strike, creep, turn to turn and layer insulation.
Second: Take the open circuit and short circuit original inductance specs and calculate the new inductances to ensure the new inductance values will not impair the xfmr application (line and load).
Third: Recalculate Watts/In^2 of cooling surface for the coils and cross-check with design specs. Recalculate new Eddy current and harmonics losses in the reverse current situation. Recalculate new watts loss (Iron loss and I^2R loss) based on reverse current flow in each coil. Depending on the rating of the insulation system you want watt loss per In^2 of surface area to be below .5 to .2 for oil filled.
Lastly: Take into account that the inrush current will either increase or decrease depending on the geometry and location of the original primary (line) side could. This could cause breaker tripping, flash over or other anomalous events on the application (load side).