An alternative to Creek's answer (whilst also using part of it) is to dispense with watch, and use the -r option to lsof instead, to end up with a repetitive log scrolling up the terminal, for example
lsof -i TCP:80,443 -r 1
which repeats every one second, and each repeat's output is separated by =======. It may not be as pretty, but it gives a scrollable history, for example:
======= COMMAND PID USER FD TYPE DEVICE SIZE/OFF NODE NAME firefox 9542 user 27u IPv4 1068219 0t0 TCP user-300V3Z-300V4Z-300V5Z:37360->192.0.78.23:https (ESTABLISHED) firefox 9542 user 48u IPv4 1053405 0t0 TCP user-300V3Z-300V4Z-300V5Z:45948->ec2-54-213-37-69.us-west-2.compute.amazonaws.com:https (ESTABLISHED) ======= COMMAND PID USER FD TYPE DEVICE SIZE/OFF NODE NAME firefox 9542 user 27u IPv4 1068219 0t0 TCP user-300V3Z-300V4Z-300V5Z:37360->192.0.78.23:https (ESTABLISHED) firefox 9542 user 48u IPv4 1053405 0t0 TCP user-300V3Z-300V4Z-300V5Z:45948->ec2-54-213-37-69.us-west-2.compute.amazonaws.com:https (ESTABLISHED) firefox 9542 user 52u IPv4 1138942 0t0 TCP user-300V3Z-300V4Z-300V5Z:57602->kul08s01-in-f10.1e100.net:https (SYN_SENT) firefox 9542 user 102u IPv4 1139934 0t0 TCP user-300V3Z-300V4Z-300V5Z:49102->kul09s13-in-f14.1e100.net:https (ESTABLISHED) firefox 9542 user 110u IPv4 1138950 0t0 TCP user-300V3Z-300V4Z-300V5Z:49104->kul09s13-in-f14.1e100.net:https (SYN_SENT) ======= ... ======= COMMAND PID USER FD TYPE DEVICE SIZE/OFF NODE NAME firefox 9542 user 27u IPv4 1068219 0t0 TCP user-300V3Z-300V4Z-300V5Z:37360->192.0.78.23:https (ESTABLISHED) firefox 9542 user 48u IPv4 1053405 0t0 TCP user-300V3Z-300V4Z-300V5Z:45948->ec2-54-213-37-69.us-west-2.compute.amazonaws.com:https (ESTABLISHED) firefox 9542 user 51u IPv4 1140129 0t0 TCP user-300V3Z-300V4Z-300V5Z:52284->kul09s13-in-f10.1e100.net:https (ESTABLISHED) firefox 9542 user 108u IPv4 1137384 0t0 TCP user-300V3Z-300V4Z-300V5Z:55886->103.229.10.236:https (ESTABLISHED) firefox 9542 user 122u IPv4 1137399 0t0 TCP user-300V3Z-300V4Z-300V5Z:55870->kul08s12-in-f1.1e100.net:https (ESTABLISHED) firefox 9542 user 126u IPv4 1137402 0t0 TCP user-300V3Z-300V4Z-300V5Z:47370->stackoverflow.com:https (SYN_SENT)
Note: I only had Firefox open, so only one application is showing.
Obviously this output could be redirected or piped to a (log) file.