the lease time is whatever the dhcp server of your isp has it set to. an ip lease can be as short as a second or as long as forever. my isp uses dhcp but my ip (or rather the ip of my router) is essentially always the same. which would mean my lease time is forever. the main reason you use dhcp, and its not security (thats more a side effect of switching addresses), is because theres a limit to how many ips a isp has allocated to them. say an isp has 10,000 ip addresses and the average usage of those addresses is 50%, this means that the isp can have more than 10,000 subscribers despite only having 10,000 addresses, since many customers arent staying connected to the net all the time. theres also the fact that dhcp makes it easy to setup new clients and the users dont have to enter any network settings most of the time.
so every time a user connects to the isp, they are leased an address from the address pool (all the unallocated addresses) and when they disconnect and/or when their lease expires, the address is put back in the pool so somone else can use it. there are ways around address limits , like using routers. there are also hard limits, like the limit of 2^32 addresses and then subnets play a roll on how many addresses you can actually use for clients (im not even gonna start trying explaining how that works, as i barely understand it myself).
eventually when the internets finally start using ipv6, then the number of potential addresses will essentially become gargantuan. then it becomes possible that everyone could have their own static address, however dhcp will most likely still be used to make managing the much larger pool of addresses easyer for administrators. as well as making setup easyer for users.
