Trying to figure the the logic behind your access list:
access-list 111 deny tcp 192.168.1.0 0.0.0.255 any eq www // deny http from inside lan
access-list 111 deny tcp 192.168.1.0 0.0.0.255 any eq 443 // deny https from inside lan
access-list 111 permit ip any any // allow anything else
Your requirements:
allow specific range from that subnet to access the internet:
You can use object groups with ranges to do that :
https://www.cisco.com/en/US/docs/ios-xml/ios/sec_data_acl/configuration/15-2mt/sec-object-group-acl.html
add the lines referring to the object groups before the first and second deny:
ip access-list ext 111
1 permit <your object>