Lemon Plant - Help needed

I have been given a lemon plant as a gift and i am growing it in my kitchen.
It seems to be growing well and has now grown 1 full sized lemon.
However there are now another 12 growing on the plant, which may cause problems both in terms of weight and using the nutrients/resources of the plant.
The information that came with the plant is useless and doesnt even tell you what type of lemon plant it is, or how to look after it.
Please could i have some advice on the large number of growing lemons and the general maintenance of the plant.
The plant is about 30cm high and wide currently.

Thanks in advance.