Otdfbt

I have a production server in which I need to move space from /data (3.7 T) to /home (50G) using lvm, I need to move around 200G of space.
The solution I'm thinking of is reducing the size of /data and then take the freed space and extend /home with it.

Adding a disk is not an option as I have an abundance of space on /data (3.7 T and only 1% of it used as shown in the df command below)

I have one volume group and one pv with no free space:

pvs:

PV VG Fmt Attr PSize PFree
 /dev/sda4 rhel lvm2 a-- 3.64t 4.00m

vgs:

 VG #PV #LV #SN Attr VSize VFree
 rhel 1 10 0 wz--n- 3.64t 4.00m

lvs output:

 LV VG Attr LSize Pool Origin Data% Meta% Move Log Cpy%Sync Convert
 data rhel -wi-ao---- 2.98t
 home rhel -wi-ao---- 50.00g
 opt rhel -wi-ao---- 30.00g
 root rhel -wi-ao---- 50.00g
 swap rhel -wi-ao---- 30.00g
 tmp rhel -wi-ao---- 200.00g
 usr rhel -wi-ao---- 100.00g
 var rhel -wi-ao---- 200.00g
 var_log rhel -wi-ao---- 10.00g
 var_log_audit rhel -wi-ao---- 5.00g

output of df -khT:

/dev/mapper/rhel-usr ext4 99G 8.7G 85G 10% /usr
/dev/sda2 ext4 976M 101M 808M 12% /boot
/dev/sda3 vfat 512M 0 512M 0% /boot/efi
/dev/mapper/rhel-home ext4 50G 41G 5.7G 88% /home
/dev/mapper/rhel-opt ext4 30G 11G 18G 39% /opt
/dev/mapper/rhel-tmp ext4 197G 4.2G 183G 3% /tmp
/dev/mapper/rhel-data ext4 3.0T 26G 2.8T 1% /data
/dev/sdb1 ext4 3.6T 79G 3.4T 3% /data/disk01
/dev/sdc1 ext4 3.6T 758M 3.4T 1% /data/disk02

The output of lsblk shows that /home and /data are both under the same partition sda4, although I don't exactly know how to do this. It seems that it's convenient that both /home and /data are under the same partition:

lsblk:
NAME MAJ:MIN RM SIZE RO TYPE MOUNTPOINT
sda 8:0 0 3.7T 0 disk
├─sda1 8:1 0 1M 0 part
├─sda2 8:2 0 1G 0 part /boot
├─sda3 8:3 0 512M 0 part /boot/efi
└─sda4 8:4 0 3.7T 0 part
 ├─rhel-root 253:0 0 50G 0 lvm /
 ├─rhel-swap 253:1 0 30G 0 lvm [SWAP]
 ├─rhel-usr 253:2 0 100G 0 lvm /usr
 ├─rhel-tmp 253:3 0 200G 0 lvm /tmp
 ├─rhel-home 253:4 0 50G 0 lvm /home
 ├─rhel-var 253:5 0 200G 0 lvm /var
 ├─rhel-var_log_audit 253:6 0 5G 0 lvm /var/log/audit
 ├─rhel-var_log 253:7 0 10G 0 lvm /var/log
 ├─rhel-opt 253:8 0 30G 0 lvm /opt
 └─rhel-data 253:9 0 3T 0 lvm /data

I need to do this without the loss of any data and preferably without restarting the server.

If this is possible please recommend a solution, if not please explain why.

ext4 doesn't support on-line shrinking, you have to unmount the filesystem before to unmount it but the operating system can remain up.
ext4 and LVM logical volume online resize(increasing the size) instead is supported.
I'm reading that you have a RHEL, so you should have access to Red Hat knowledge base Red Hat.
This solution https://access.redhat.com/solutions/32530 describe the procedure to shrink a LVM logical volume with ext4 filesystem on it.