Or is it something that could be easily done without the use of modules?

I'm deeply suspicious of questions that seem too easy, but ...

It kinda depends what form you have or obtain the lower-triangle matrix in to start.

But assuming you've loaded the LT matrix into a 2d array, then "converting to a square matrix" consists of padding the upper triangle with zeros, which is one line of perl:

#! perl -slw
use strict;
use Data::Dump qw[ pp ];

sub fillLTM {
    my @lt;
    my $n = 1;
    push @lt, [ splice @_, 0, $n++ ] while @_;
    return @lt;
}

## read raw data
while( my $rawData = <DATA> ) {
    ## Populate LT matrix
    my @lt = fillLTM( split ' ', $rawData );
    pp \@lt;;

    ## Pad to square matrix
    push @{ $lt[$_] }, (0)x( @{ $lt[-1] } - @{ $lt[$_] } ) for 0 .. $#
+lt -1;;
    pp \@lt;;
}

__DATA__
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
[download]

Produces:

C:\test>junk
[
    [1],
    [2, 3],
    [4, 5, 6],
    [7, 8, 9, 10]
]
[
    [1, 0, 0, 0],
    [2, 3, 0, 0],
    [4, 5, 6, 0],
    [7, 8, 9, 10]
]

[
    [1],
    [2, 3],
    [4, 5, 6],
    [7, 8, 9, 10],
    [11, 12, 13, 14, 15]
]

[
    [1, 0, 0, 0, 0],
    [2, 3, 0, 0, 0],
    [4, 5, 6, 0, 0],
    [7, 8, 9, 10, 0],
    [11, 12, 13, 14, 15]
]
[download]