Does a females spiders lay eggs?

Yes they can very easily. Check corners either on the floor or on the ceiling where they could make sturdy webs and you could possibly find an egg sack (it looks like a very small cotton ball about the size of a peanut). Any bug spray will work to kill the eggs but might I suggest, you could relocate the egg sack and the spider outside in a flowerpot or somewhere safe so that the creatures can go on living. Thank you if you choose the latter suggestion, I couldn't bear the thought of killing such harmless creatures.