Example using loops and regular expressions

loopy.bash

#!/bin/bash

# I personally would merge sample across lane. Gzip file can just be concated
# together and as long as R1 and R2 are done in the same order it should work
# fine.
#
# going from
# - 1860_Time_0_S1_L001_R1_001.fastq.gz
# - 1860_Time_0_S1_L002_R1_001.fastq.gz
# - 1860_Time_0_S1_L002_R1_001.fastq.gz
# - 1860_Time_0_S1_L004_R1_001.fastq.gz
# to
# - 1860_Time_0_R1.fastq.gz
pattern='([[:digit:]]+)_(Time_[[:digit:]]+)_(S[[:digit:]])_(L[[:digit:]]{3})_(R[12])_001.fastq.gz'
for file_name in *_001.fastq.gz
do
  [[ "$file_name" =~ $pattern ]]
  sample_name="${BASH_REMATCH[1]}"
  time="${BASH_REMATCH[2]}"
  lane="${BASH_REMATCH[4]}"
  read="${BASH_REMATCH[5]}"
  cat $file_name >> "${sample_name}_${time}_${read}.fastq.gz"
done

# Then we can do the same thing but iterate over the new files only. Since I
# want R1 and R2 together, I will just iterate over the new R1s.
#
pattern2='(.*)_R1.fastq.gz'
for file_name in *R1.fastq.gz
do
  [[ "$file_name" =~ $pattern2 ]]
  prefix="${BASH_REMATCH[1]}"
  read1="${prefix}_R1.fastq.gz"
  read2="${prefix}_R2.fastq.gz"
  /usr/local/usrapps/florfenicolamr/fastp \
    -i $read1 -I $read2 \
    -o "new${prefix}_R1.fastq.gz" -O "new${prefix}_R2.fastq.gz" \
    -l 36 \
    -c \
    -f 4 -F 4 \
    -t 4 -T 4 \
    -m --merged_out "${prefix}_merged.fastq.gz" \
    --unpaired1 "${prefix}_U1.fastq.gz" --unpaired2 "${prefix}_U2.fastq.gz" \
    -h "${prefix}.html"
done