How to run eval with lockf command?

I have a command which I run via eval as shown below.

#! /bin/sh

readonly scr="MYENV=1 sh /tmp/scr.sh"

eval ${scr} -a 1 -b 2

Now I want to run the scr script with lockf utility, so I made the following changes:

#! /bin/sh

readonly scr="MYENV=1 sh /tmp/scr.sh"

lockf -k /tmp/f.lock eval ${scr} -a 1 -b 2

This throws the following error:

lockf: eval: No such file or directory

Basically the limitation is the MYENV=1 which needs to be exported while running the command (thus the use of eval). I'm a beginner in shell programming and am unsure on how to get around this. How do I make this work?