MLB created divisions in 1969 and added the LCS playoff round. NBC held the national TV rights to these games, but its LCS coverage in those first years left much to be desired.
At the time, the best-of-5 LCS began on a Saturday for both leagues and NBC would kick things off with an afternoon doubleheader. Then things would get interesting. On Sunday, NBC typically selected one of the baseball games for a national telecast and presented a "football/baseball" doubleheader with regional NFL action at 1 pm and an LCS game at 4. The other LCS game was relegated to a local telecast. Neither MLB nor the NFL scheduled any games for Sunday night at the time.
When both leagues played on the same weekday, the starting times overlapped by 1.5 hours. NBC would televise one game in full in the early afternoon and then join the late game in progress.
The standard practice for NBC was to send its top announcer team of Curt Gowdy and Tony Kubek to the weekend games of one LCS and then shift them to the opposite league for the weekday games. Jim Simpson handled play-by-play duties for the other series from 1969-1974 with Joe Garagiola filling that role in 1975. The "B" team analysts were Sandy Koufax (1969-1972) and Maury Wills (1973-1975).
During this era, MLB typically scheduled these playoff series with no off day for travel unless one of the teams was from the west coast. And the game times were fixed in advance with no provisions for moving a start later in the day if the other series ended early.
For example, check out the NBC TV schedule for the 1972 LCS round (all times ET):
Sat 10/7, Reds @ Pirates, NLCS game 1, 1 pm, Simpson, Koufax
Sat 10/7, Tigers @ Athletics, ALCS game 1, 4 pm, Gowdy, Kubek
Sun 10/8, Tigers @ Athletics, ALCS g2, 4 pm, Gowdy, Kubek
(Note: NBC did not carry NLCS g2 which started at 1 pm and was only televised locally.)
Mon 10/9, Pirates @ Reds, NLCS game 3, 3 pm, Gowdy, Kubek
Tue 10/10, Athletics @ Tigers, ALCS game 3, 1:30 pm, Simpson, Koufax
Tue 10/10, Pirates @ Reds, NLCS game 4, (joined in progress - 3 pm first pitch), Gowdy, Kubek
Wed 10/11, Athletics @ Tigers, ALCS game 4, 1:30 pm, Simpson, Koufax
Wed 10/11, Pirates @ Reds, NLCS game 5, (joined in progress - 3 pm first pitch), Gowdy, Kubek
Thu 10/12, Athletics @ Tigers, ALCS game 5, 1:30 pm, Simpson, Koufax
After the successful 1971 experiment to move one World Series game to prime time, MLB began scheduling all weekday World Series games at night. But for some reason, MLB continued to keep all the weekday LCS games in the afternoon. It wasn't until 1975 that MLB moved any LCS game to prime time (when it provided regional coverage of game 3 of each series on a Tuesday night).
Because of the incomplete national TV coverage, NBC allowed the participating markets to carry the LCS telecasts using local announcers. So fans in those markets would have access to each game in its entirety (and had a choice of which telecast to watch when NBC also aired the game).
In 1976, for the first time, MLB placed each LCS game into a unique national TV window and scheduled one game for prime time each day including Sunday. The practice allowing for separate LCS telecasts with local announcers continued through 1983.
Sadly, very little NBC footage survived from these early LCS years. Much of 1973 NLCS game 1 exists as well as portions of the 1972 ALCS game 2 telecast.
Here is the earliest LCS footage I have found - a few clips of Gowdy calls from the 1969 NLCS: