Was it known that $\mathsf{LTIME \subsetneq NLTIME}$?
The other answer is quite misleading. The classes $\mathrm{DTIME}(\log n)$ and $\mathrm{NTIME}(\log n)$, usually denoted DLOGTIME and NLOGTIME, do indeed have a sensible and well-accepted meaning in the literature. 

When discussing sublinear time classes (deterministic, nondeterministic, alternating, etc.), it is standard to use a Turing machine model that does not have an input tape, but a query tape on which one can write (in binary) the index of an input position, and obtain the input symbol at that position by entering a special state. (The query tape is not cleared or otherwise modified after a query.) This is essentially the same mechanism as used by oracle Turing machines, and the model is sometimes called the random-access Turing machine.

And yes, it is known that $\mathrm{DLOGTIME\subsetneq NLOGTIME}$: a simple NLOGTIME language not recognizable in DLOGTIME is
$$L=\{w\in\{0,1\}^*: \text{$w$ has at least one $1$ at some position}\}.$$
There are unconditional separations like this even for some bigger classes, for example $\mathrm{AC^0}$, whose uniform version coincides with languages recognizable by an alternating TM in time $O(\log n)$ with $O(1)$ alternations.