package mysql-client-5.7 (not installed) failed to install/upgrade: trying to overwrite '/usr/bin/myisam_ftdump', which is also in package mariadb-server-10.0 10.0.29-0ubuntu0.16.10.1

Hi,
for what I see in the logs you are trying to install mysql AND mariadb on one system.

They are mutually exclusive as they provide the same service but with different implementations.
Therefore e.g. with a mysql installed asking to install mariadb gives you

$ apt-get install mariadb-server mariadb-client
  [...]
  The following packages will be REMOVED:
    mysql-client mysql-client-5.7 mysql-client-core-5.7 mysql-server mysql-server-5.7 mysql-server-core-5.7

That said I'd expect there to never be an issue with the same file provided as they exclude each other anyway.
Trying to reproduce:
ii mysql-client 5.7.17-0ubuntu0.16.10.1
ii mysql-common 5.7.16-0ubuntu0.16.10.1
ii mysql-server 5.7.17-0ubuntu0.16.10.1
$ apt-get install mariadb-server mariadb-client

Working as expected, removing the conflicting bits before installing mariadb.
I tested on Yakkety just as your reported system is.

Is there anything special on your systems configuration or your current install/upgrade that might cause this?

I see in your log that you did:
$ apt-get -o APT::Status-Fd=4 -o APT::Keep-Fds::=5 -o APT::Keep-Fds::=6 -q -y -o APT::Install-Recommends=true -o APT::Get::AutomaticRemove=true -o APT::Acquire::Retries=3 install lamp-server

With mariadb installed before, so doing that as well.
$ sudo apt-get install tasksel
$ sudo tasksel install lamp-server
Interesting it failed for me as well.

Eventually that comes down to:
$ apt-get install apache2 mysql-server

Ok, lets round this up to a simplified repro:
$ lxc launch ubuntu-daily:yakkety/amd64 yakkety-maria-collision
$ lxc exec yakkety-maria-collision bash
$ apt-get update
$ apt-get install mysql-server
$ apt-get install mariadb-server
$ apt-get install mysql-server

There I can see:
Aborting downgrade from (at least) 10.0 to 5.7.
If are sure you want to downgrade to 5.7, remove the file
/var/lib/mysql/debian-*.flag and try installing again.

But even if doing so I run into several issues like:
ERROR: Unable to start MySQL server:
2017-02-06T10:10:08.165223Z 0 [ERROR] unknown variable 'myisam-recover=BACKUP'
2017-02-06T10:10:08.168262Z 0 [ERROR] Aborting

I don't know enough on the two-way up/downgrade between mariadb and mysql, subcribing Lars&Robie for their expertise.