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Got here a list of columns, as follows:

59 LOUIS 1202 +1
60 FREDDIE 1201 +4
61 FINLAY 1200 -2
62 LEON 1137 +12
63 HARLEY 1132 +6
64 DAVID 1127 -1
65 MOHAMMAD1100 +6
66 REECE 1095 -1
67 KIAN 1090 0
68 KAI 1056 -6
69 KYLE 1030 -18
70 BRANDON 1011 -4
71 HAYDEN 1006 +5
72 ZACHARY 995 +10
73 KIERAN 973 -12
73 LUCA 973 -1
75 ASHTON 954 +4
76 BAILEY 939 -6
77 JAKE 913 +10
78 GABRIEL 910 +14
79 SAM 900 -2
80 EVAN 890 0
81 BRADLEY 847 -13

How could be extracted only the lines with, for example, letter "L", as follows:

73 LUCA 973 -1

That seems to be duplicated, but anyway, if it was understood, one may do it as follows:

First, save the list in a some nameslist.txt file, then:

sed -rn '/^[^s]+s+[F]/p' list.txt > result.txt, which should return following output in result.txt file:

60 FREDDIE 1201 +4
61 FINLAY 1200 -2

awk '$2 ~ /^L/' file

Tells awk to test the second field $2 using the regex ~ expression ^L and print the matching lines.

The regex matches any field (string) that starts ^ with an L

Building on @bu5hman's answer: With awk, you can easily pass the letter as a parameter:

awk -v letter="L" 'substr($2, 1, 1) == letter' file
# or with a constructed regex
awk -v letter="L" '$2 ~ "^" letter' file

Assuming that you have that list in list.txt, you can do the following:

 grep -h L list.txt > list_L.txt 

Explanation: grep L list.txt gives you all the lines containing an uppercase L. The option -h suppresses the output of the file name, but is only necessary if you are searching through multiple files (e.g. grep -h L lis*.txt). Adding > list_L.txt redirects the lines to the specified file.

If the L must only occur at the beginning of a "word" (on name, in this case), you need to tweak the above command a bit:

 grep -h '<L' list.txt > list_L.txt 

Adding < matches the beginning of a "word", so <L selects lines containing a word beginning with an uppercase L.

Another grep example:

grep -E "[0-9]+ +L" file

+ matches one or more occurrence of the previous character, so in this case we match at least one numeric character, and at least one space, followed by a capital L.

-E is required to interpret the + as a special character instead of a literal '+'

output:

59 LOUIS 1202 +1
62 LEON 1137 +12
73 LUCA 973 -1

Avoid RegEx when possible. AWK example:

index($2, "L") == 1