So list Sengoku and Nobunaga do have a limitation up to 8 mounted bushi MAX

It seems to aim the mounted PB bushi but as written will also impact a TAKEDA List.

If TAKEDA is taken as ally will the number of mounted lancers be limited by the number of Bushi in the sengoku / Nobunaga lists ?

The reverse is clearly written

The lists say what they intend.  The limitation doesn't work in reverse.

Richard