Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
1- It is a Muslim’s duty to well observe all the things he/she uses to be from a lawful (halal) source.
2- If you have alternatives to soaps or lotions that contain alcohol or lard, it is better to avoid them. However, using such products is not haram (prohibited) according to some Muslim scholars.
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
It is best to avoid such products if you have alternatives. Although it is not considered haram to use them, according to the rulings of eminent scholars, for two reasons:
First, they are not meant for consumption; strictly speaking, the texts are explicitly referring to their consumption and not external use.
Second, these elements, in the process of production, have undergone chemical transformation so that the original ingredients have been wholly changed, and, thus, according to the principles of jurisprudence, they are to be judged differently.
It is, therefore, analogous to alcohol turned into vinegar; while the former is haram, the latter is not.
Allah Almighty knows best.