Let's be sure not to confuse 'LAN' with 'WAN' as they are separate networking concepts. 'LAN' refers to your local network, inside your router/gateway/modem, etc. 'WAN' refers to the network between your router/gateway and the remote router/gateway you connect to (in theory, can be dozens simultaneously depending on application traffic).
Your 'LAN' speed isn't the issue here; it's your ISP WAN connectivity that is in play when you are referring to internet latency, high pings and download speeds. Also remember that advertised ISP speeds (and what you are paying for each month) varies widely based on localized traffic to hubs in your area as well as the ability of the remote router/gateway/server to process data effectively.
The...