No, lanolin. Lanolin is an oil made from wool. It seem to work well for the sheep, they never complain that the wool is too itchy.
Another vote for Palmolive. While it's not as aesthetically pleasing as the pricier stuff nothing performs better at any price. For me at least.
I'll echo the OP and name Nivea Original, but I'll combine it with Nivea Splash. Both to be had for less than $10 and not only it's my favourite cheap cream, I can say it's on par with way more expensive creams, and will continue to be a staple in my den.
The only problem is you need a tube of shaving cream with the small opening it won't take our regular tubes like proraso or Nivea. But I love the Old Spice shave cream and it's readily available really cheap
Cremo Cooling, around $6 locally. Lathers up just fine for me. I dig it. Arko was 1st place but now 2nd. I only got that from a Travel Box so I'm not sure how "budget" it is. Palmolive (also from the T.B.) was quite usable but not as good for me as Arko. I do want to try the O.S. lime someday.
Kiss My Face.....I prefer this to the few that I have tried (Proraso Blue,Speick,Cremo), and a bottle seems to last a very long time. Around 5-6 months of every other day shaving as I prefer or 2 1/2 to 3 months of daily shaving. Like the Key Lime & Lavender scents the best. I pay between $5.19-$5.95 for 11oz from either Vitacost or Lucky Vitamin (I usually order other items with the shave cream to get free shipping).
Palmolive, Colgate, and the "orginial " Rise....3 creams I miss badly. (I do like the reformulated Rise, but it isn't the same joy).
For me, Proraso Blue. Ya can get it for $10.00 shipped. Great lather, mysterious scent....makes me take off the cap and take a sniff.