Lehmer random number generator cipher - looking for differentials
Do you see any differentials here?

Yes; consider a differential where one side is the value $X$ and the other side is the value $2^{127}-X$.
Your cipher consists of three operations:

Multiplying the current value by an odd value $a_i$ modulo $2^{128}$

This operation preserves the differential with probability 1; one side would evaluate to $a_i \cdot X$ and the other side would evaluate to $a_i \cdot (2^{127} - X) = a_i \cdot 2^{127} - a_i \cdot X = 2^{127} - a_i \cdot X$

Negating the current value (which is done as a part of rounds 2-10)

This operation preserves the differential with probability 1; this happens because $-(2^{127} - X) = 2^{127} - (-X)$

Reversing the bits in the current value

This operation preserves the differential with probability 0.5; namely, if the lsbit of $X$ (equivalently, $2^{127} - X$) is a 1.  This happens because, when the lsbit is a 1, this relationship is equivalent to the relation that $X \oplus (2^{127}-X) = 2^{127}-2$.  This later relation is preserved when you reverse the bits, and hence the former one is as well.
This gives you a differential that holds with probability $2^{-10}$ through the ten rounds of the cipher.