These are general names of technology and do not represent speeds.
TYPICALLY - LAN speeds are higher than higher than DSL.
Depending on what LAN speed you have, it is possible to get a broadband connection that is "faster".
Typically, a home user will have a 10Mbps or 100 Mbps wired LAN speed, 1000Mbps and 10Gbps are available but are typically used in businesses, not homes.
DSL maxes out at a lower rate of speed than a cable modem. But both are considered "broadband" connections.
So, if you purchase a 20Mbps cable modem service and have only a 10Mbps home LAN speed, the cable modem will be faster. In fact, you would never be able to use the entire bandwidth of the cable modem. Your top speed will always be as fast as the slowest point in the connection.
If you use IEEE 802.11b wireless - its top speed is 2Mbps.
IEEE 802.11g & a wireless top out at 54Meg
IEEE 802.11n which isn't a formal standard yet, tops out at 300Mbps.