Can Oxybuprocaine hydrochloride react with lidocaine hydrochloride? To anaesthetise the mucous membrane 2 separate drugs were given topically:

Oxybuprocaine hydrochloride and Lidocaine hydrochloride. The reason to use both of them seem to be beginning of action and its duration (the former starts faster but shorter, the latter starts later but longer acting).

If instead having them in separate bottles they will be mixed in one, would it cause any interactions between them?

oxybuprocaine:
Looking at the functionality, oxybuprocaine looks more likely to react with itself rather than lidocaine. As it's a salt and also no doubt from numerous medical trials, this doesn't occur,  the anticipation would be that the two compounds would be fine.  The $pK_a$'s of the tertiary amines would also be expected to be similar, so one shouldn't neutralise the other.