Thank you @Zhiming_Liu; The solution you provided worked. I did the following changes in the imx-system-manager code related to lpuart3 along with my device tree changes and build a new yocto image. ttyLP2 was in the /dev/ and I also used it in my application and was also running successfully.
Changes in imx-system-manager code:
--- a/configs/mx95evk.cfg
+++ b/configs/mx95evk.cfg
@@ -370,7 +370,6 @@ LPIT1 OWNER
LPTMR1 OWNER
LPTMR2 OWNER
LPTPM1 OWNER
-LPUART3 OWNER, test
MSGINTR1 OWNER
MSGINTR2 OWNER
MU5_A OWNER
@@ -477,6 +476,7 @@ PERLPI_GPIO3 ALL
PERLPI_GPIO4 ALL
PERLPI_GPIO5 ALL
PERLPI_LPUART1 ALL
+PERLPI_LPUART3 ALL
PERLPI_LPUART4 ALL
PERLPI_LPUART5 ALL
PERLPI_LPUART6 ALL
@@ -760,6 +760,7 @@ LPTPM4 OWNER
LPTPM5 OWNER
LPTPM6 OWNER
LPUART1 OWNER
+LPUART3 OWNER
LPUART4 OWNER
LPUART5 OWNER
LPUART6 OWNER
my /dev directory
root@imx95:~# ls -al /dev/ttyLP2
crw-rw---- 1 root dialout 241, 2 Sep 7 14:30 /dev/ttyLP2
root@imx95:~# dmesg | grep ttyLP2
[ 2.426195] 42570000.serial: ttyLP2 at MMIO 0x42570010 (irq = 141, base_baud = 1500000) is a FSL_LPUART