He feels that God's love has conditions attached to it - conditions like our attitude to God, our willingness to repent of our sins, etc.
I guess he is correct in the sense that the Bible does not have the phrase 'unconditional love' in its text. But neither does it have the word 'sovereignty' or 'universal' or 'evangelical' or several other English words that we use to express a Biblical concept or theological idea. It is the concept or idea that is important and that needs to be based on Scripture, not whether an English word that English-speaking people use to describe that concept is in the Bible.
My evidence for God's 'unconditional' love? Just a few brief references.
But God demonstrates his own love for us in this: While we were still sinners, Christ died for us. [Rom 5 : 8]
For Christ's love compels us, because we are convinced that one died for all, ... [2 Cor 5 : 14]
When we were still powerless, Christ died for the ungodly. [Rom 5 : 6]
Jesus said, "Father, forgive them, for they do not know what they are doing." [Luke 23 : 34]
Consequently, just as one trespass resulted in condemnation for all people, so also one righteous act resulted in justification for all people. [Rom 5 : 18]
But I tell you, love your enemies and pray for those who persecute you, that you may be children of your Father in heaven. He causes his sun to rise on the evil and the good, and sends rain on the righteous and the unrighteous.
[Matt 5 : 44, 45]
I use the term 'unconditional' to mean constant, dependable, (which are probably unbiblical words also) just like the sun is constant and doesn't depend on conditions outside of itself to determine whether it radiates heat and light or not. Sometimes we see or feel the sun differently because of overcast conditions or we are indoors, but the sun is still the same, doing the same thing all the time. Its performance (character) remains constant - it is in this sense that I would say it is unconditional, even though how we experience it is dependant on certain conditions.
In a similar way, how things experience the sun is dependant on their personal condition. For example, sun shining on clay and ice-cream produces very different effects. The condition of the recipient determines the outcome, in the same way, as my friend points out, that people in different conditions experience blessing or discipline or hardship under exposure to the love of God.
In summary I believe God's love is unconditional (constant, perfect, reliable) even though it produces different effects due to the different conditions on which it falls. For me, God's love is always perfect, operating for our good, whether in blessing or hardship, as it works all things towards God's predetermined glorious end.
What is your opinion of using 'unconditional' in this way?