unfortunately the ppa solve also not the behind a proxy problem.
usualy in my produktion in front (bastion/proxy host) is debian 9
so i test both with debian 9 and ubuntu 18.04 ppa at on the proxy
host.

i modified a littel the configuration to get closer for the
production env.

VM with LB Manager IP:192.168.56.211

i start again with the old apache version

:~# apt-get install libapr1 libaprutil1 libaprutil1-dbd-sqlite3 libaprutil1-ldap liblua5.2-0
:~# dpkg -i apache2_2.4.29-1ubuntu4.8_amd64.deb apache2-bin_2.4.29-1ubuntu4.8_amd64.deb apache2-data_2.4.29-1ubuntu4.8_all.deb apache2-utils_2.4.29-1ubuntu4.8_amd64.deb

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:~# vim /etc/apache2/sites-available/management.conf
<VirtualHost 192.168.56.211:81 127.0.0.1:81>
    Servername 127.0.0.1
    ServerAdmin root@localhost

    <Location /balancer-manager>
        SetHandler balancer-manager
        Require local
        #Require ip 192.168.56.0/24 127.0.0.1/24
        Require all granted
    </Location>

    <Location /test-web01/balancer-manager>
        SetHandler balancer-manager
        Require local
        #Require ip 192.168.56.0/24 127.0.0.1/24
        Require all granted
    </Location>

    LogLevel warn
    ErrorLog ${APACHE_LOG_DIR}/management_error.log
    CustomLog ${APACHE_LOG_DIR}/management_access.log combined

</VirtualHost>

# vim: syntax=apache ts=4 sw=4 sts=4 sr noet

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:~# vim /etc/apache2/sites-available/proxytest.conf
<Proxy "balancer://test">
        BalancerMember "http://192.168.168.130/test"
        BalancerMember "http://192.168.168.131/test" status=+H
        ProxySet lbmethod=bybusyness
</Proxy>

<VirtualHost 127.0.0.1:8100>
ServerAdmin root@localhost
ServerName testapp01
ServerAlias 127.0.0.1:8100

    ProxyPass           "/test" "balancer://test"
    ProxyPassReverse    "/test" "balancer://test"

    CustomLog ${APACHE_LOG_DIR}/test-access.log combined
    ErrorLog  ${APACHE_LOG_DIR}/test-error.log

</VirtualHost>

# vim: syntax=apache ts=4 sw=4 sts=4 sr noet

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:~# a2enmod proxy_balancer proxy_http lbmethod_bybusyness lbmethod_byrequests
:~# a2ensite management proxytest

:~# vim /etc/apache2/ports.conf
[...]
Listen 81
Listen 8100

:~# systemctl restart apache2

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check localhost LB Manager

:~# apt-get install lynx

:~# lynx 127.0.0.1:81/balancer-manager
:~# lynx 127.0.0.1:81/test-web01/balancer-manager

:~# tail -f /var/log/apache2/management_error.log
-> worked as expectet
-> no log entries on the LB Manager VM

-------------------------------------------------------------------------

Bastion Host Proxy VM IP:192.168.56.230

:~# apt-get install apache2 lynx

check from proxy VM that LB Manager is working without a proxy config in
front of them.

:~# lynx 192.168.56.211:81/balancer-manager
:~# lynx 192.168.56.211:81/test-web01/balancer-manager

:~# tail -f /var/log/apache2/management_error.log
-> no log entries on the LB Manager VM

start proxy configuration

:~# vim /etc/apache2/sites-enabled/000-default.conf
[...]
       <Location /test-web01>
                ProxyPass        http://192.168.56.211:81/test-web01
                ProxyPassReverse http://192.168.56.211:81/test-web01
                SetOutputFilter  INFLATE;SUBSTITUTE
                Substitute "s|http://192.168.56.230:81|http://192.168.56.211|i"
       </Location>
[...]


:~# a2enmod proxy_http substitute

:~# systemctl restart apache2


check over the proxy configuration

:~# lynx 192.168.56.230/test-web01/balancer-manager

Browser: Firefox and Chrome

http://192.168.56.230/test-web01/balancer-manager

everything is working 

:~# tail -f /var/log/apache2/management_error.log
-> no log entries on the LB Manager VM

-------------------------------------------------------------------------

apache update the VM with LB Manager

:~# apt-get update
:~# apt-get upgrade

:~# dpkg -l | grep apache2
ii  apache2        2.4.29-1ubuntu4.10
ii  apache2-bin    2.4.29-1ubuntu4.10
ii  apache2-data   2.4.29-1ubuntu4.10
ii  apache2-utils  2.4.29-1ubuntu4.10

-> reboot the VM

start all test with tail on the error log

:~# lynx 127.0.0.1:81/test-web01/balancer-manager

:~# tail -f /var/log/apache2/management_error.log
[Tue Sep 10 15:43:57.466767 2019] [proxy_balancer:error] [pid 880:tid 139671053002496] [client 127.0.0.1:38304] AH10187: ignoring params in balancer-manager cross-site access
[Tue Sep 10 15:44:15.946960 2019] [proxy_balancer:error] [pid 880:tid 139671019431680] [client 127.0.0.1:38308] AH10187: ignoring params in balancer-manager cross-site access


Browser: Firefox, Chrome

http://192.168.56.230/test-web01/balancer-manager

[Tue Sep 10 15:44:51.081605 2019] [proxy_balancer:error] [pid 880:tid 139671027824384] [client 192.168.56.230:56224] AH10187: ignoring params in balancer-manager cross-site access

[Tue Sep 10 15:45:15.331258 2019] [proxy_balancer:error] [pid 879:tid 139671027824384] [client 192.168.56.230:56226] AH10187: ignoring params in balancer-manager cross-site access, referer: http://192.168.56.230/test-web01/balancer-manager
[Tue Sep 10 15:45:16.351759 2019] [proxy_balancer:error] [pid 879:tid 139671036217088] [client 192.168.56.230:56226] AH10187: ignoring params in balancer-manager cross-site access, referer: http://192.168.56.230/test-web01/balancer-manager?b=test&w=http://192.168.168.131/test&nonce=33659ac6-4210-7724-90d9-306f4b21ed19

-> in the Browser test no second part is coming up for edit things

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add the ppa 

:~# add-apt-repository ppa:sbeattie/lp1842701
 apache test fixes for LP: #1842701
 Mehr Informationen: https://launchpad.net/~sbeattie/+archive/ubuntu/lp1842701
[ENTER] drücken zum Weitermachen oder Strg-c, um das Hinzufügen abzubrechen.

:~# apt-get update
:~# apt-get upgrade

:~# dpkg -l | grep apache2
ii  apache2        2.4.29-1ubuntu4.11~lp1842701
ii  apache2-bin    2.4.29-1ubuntu4.11~lp1842701
ii  apache2-data   2.4.29-1ubuntu4.11~lp1842701
ii  apache2-utils  2.4.29-1ubuntu4.11~lp1842701

-> reboot

start all test with tail on the error log

:~# lynx 127.0.0.1:81/test-web01/balancer-manager
-> is working

:~# lynx 192.168.56.211:81/test-web01/balancer-manager
-> from the proxy Machine withou proxy config is working

:~# lynx 192.168.56.230/test-web01/balancer-manager
-> from the proxy machine over the proxy configuration the first connect

[Tue Sep 10 15:54:25.988985 2019] [proxy_balancer:error] [pid 871:tid 140096665810688] [client 192.168.56.230:56244] AH10187: ignoring params in balancer-manager cross-site access, referer: http://192.168.56.230/test-web01/balancer-manager

but i can update load etc.

Now with the Browser: Firefox, Chrome

http://192.168.56.230/test-web01/balancer-manager

-> first connect no entry but i can't edit further klicks i get in the error
log and no second part for editing popscomes up.

[Tue Sep 10 15:56:25.781417 2019] [proxy_balancer:error] [pid 870:tid 140096615454464] [client 192.168.56.230:56258] AH10187: ignoring params in balancer-manager cross-site access, referer: http://192.168.56.230/test-web01/balancer-manager
[Tue Sep 10 15:56:27.002919 2019] [proxy_balancer:error] [pid 870:tid 140096607061760] [client 192.168.56.230:56258] AH10187: ignoring params in balancer-manager cross-site access, referer: http://192.168.56.230/test-web01/balancer-manager?b=test&w=http://192.168.168.130/test&nonce=d70c1e3e-e383-6138-3fdf-d4e865c18ca3
[Tue Sep 10 15:56:27.962103 2019] [proxy_balancer:error] [pid 870:tid 140096573490944] [client 192.168.56.230:56258] AH10187: ignoring params in balancer-manager cross-site access, referer: http://192.168.56.230/test-web01/balancer-manager?b=test&w=http://192.168.168.131/test&nonce=d70c1e3e-e383-6138-3fdf-d4e865c18ca3


thx again horst