How much voltage and mili amps is required to charge this battery?

you need about 1.5 volts. 40 mA will charge it in 2.5 hours, but that is a bit fast to charge a battery without any control on charge or any shutoff when fully charged.

Get a multimeter so you know the voltage and current. If need be, put in a series resistor to limit the charge rate to something safe like 10 ma.

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Normally you don't charge a battery over 10% of its MAH capacity. So charge it at 10 milliamps. You will need to use ohm's law to calculate the dropping resistor needed. (V solar panel - 1.2 Volts)/0.01 = dropping resistor in ohms. The panel must put out more than 1.2 volts to charge the battery.

Your battery doesn't sound quite right. Li would be Lithium. However, I don't recognize the -mh suffix although it could be Hydride. The two don't go together. Lithium has a voltage of between 3 and 3.7v so if it is Lithium, the cell voltage is not correct.

This voltage is quite important as you are asking about recharging from a solar cell. The voltage to recharge the cell must be higher than the voltage from the battery. A solar cell charger for a Ni-Mh cell is different to a solar cell charger for a Li-ion cell. The Lithium charger would have more cells.

Taken on face value, you need to recharge for a longer time than the ampere/hour capacity of the cell shows. About 130%. So your 40mA/h charger would need to charge for about three and a quarter hours (from fully discharged). Any other discharge level would have to be estimated based on this time.