How to use a variable as entry parameter of all_products[] to access product in Liquid

In that case, you can try assigning the value of last_name to a variable and then use that variable to access the product:

{% assign product_handle = customer.last_name %}
{% assign product = all_products[product_handle] %}

{%- if product != nil -%}
  {{ product.title }}
{%- else -%}
  Product not found
{%- endif -%}