Is it possible to consistently connect to a 220 volt network Two lamps of the same power, each rated for 110 volts.

Yes you can.
Let’s prove:
With a serial connection, U = U1 + U2, where U is the total voltage of 220 V = U1 is the voltage on the first light bulb, U2 is the voltage on the second light bulb.
Let us express the voltages across the elements in terms of current and resistance, according to Ohm’s law:
U1 = I1 * R1
U2 = I2 * R2
With a series connection I1 = I2 = I (the same current flows through all the elements), R1 = R2 – by condition. We get the following:
U1 = U2 = U / 2 = 220/2 = 110 V

Answer: Each bulb will have 110 V, which means you can connect two bulbs in series at 110 V, instead of one at 220 V.