Allright,here's the long answer why you or anybody else should not do this,its a huge fire hazard

,you need to understand electricity & the principals behind it before you leap into this,this is not the safest advice your getting here.Soldering the connection has nothing to do with it being safe nor does wire nuts or electrical tape.
The danger here comes in two forms,the first being from pulling too much wattage/amperage from the lamp cord,when you have both lights running off the same cord spliced together it pulls double the current of what the cord was designed to safely handle,have you ever felt a hot extension cord from being overloaded???? this will be the same effect.
The 2nd part of the danger will come from the connection point,irregardless if the connection is solder'ed or not connections of any type generate heat,this is why even a single connection point is supposed to be incased inside a junction box,double connections like you propose are against building codes in every state in the USA & for good reason,tons of people burn their houses down every year doing shit like that.
Can you tell me why you cant simply run 2 cords, or at the very least spend $3 on a 3 way insulated splitter ?
There should be a sticky thread on this site about electrical saftey,especially when people are growing inside closets & confined spaces,doing this on the advice of others who have had no ill effects is nuts & a huge fire waiting to happen.
Read this thread.
https://www.rollitup.org/grow-room-design-setup/41568-almost-burnt-down.html